bluuebunny/crossref_metadata_2025 huggingface dataset:
Regime Shifts and Volatility Dynamics in the Bucharest Stock Market: a Markov Switching and Arch Perspective
Authors: Tabara Genia-Iulia
Published: December 2024

This research examines the changes in volatility and shifts in regimes within the Bucharest Stock Exchange (BSE) by analysing the performance of the BET index. By utilizing both the Markov Switching Model (MSM) and Autoregressive Conditional Heteroskedasticity (ARCH) tests, the study detects two separate market conditions—bullish and bearish—and affirms the existence of volatility clustering in the Romanian market. The analysis of MSM shows a strong level of continuity in both market conditions, leading to important consequences for how investors act, such as excessive reaction, following the crowd, and fear of risk. The ARCH test emphasizes changing volatility over time, showing that market fluctuations are strongly affected by how investors collectively react to market conditions, especially in times of uncertainty or crisis. These results highlight the importance of considering behavioural biases when evaluating risk and making investment choices in emerging markets, such as Romania, for investors and policymakers. The research adds to the body of behavioural finance knowledge by offering an understanding of how investor sentiment impacts volatility and market regime shifts in emerging markets.
Asymptotic analysis of the transient Vlasov–Poisson system for a plane diode
Authors: Alabau F. , Hamdache K. , Peng Y.J.
Published: December 2024

We consider, in the nonsteady‐state case, the problem of emitted charged particles in a plane diode. This problem is described by the Vlasov–Poisson system with singular data converging to some Dirac measures in the velocity space concentrated at $t = 0$ . Under a sufficient condition on the data, which implies that the particles emitted from the cathode are all collected by the anode, we prove that the solutions converge to a measure solution, with support on velocity, of the Vlasov–Poisson system.
Two‐scale convergence and homogenization on $BV(\varOmega)$
Authors: Amar M.
Published: December 2024

We extend the notion of two‐scale convergence introduced by G. Nguetseng and G. Allaire to the case of sequences of bounded Radon measures. We prove a compactness result for two‐scale convergence. We then apply it to the study of the asymptotic behaviour of sequences of positively 1‐homogeneus and periodically oscillating functionals with linear growth, defined on the space $BV$ of the functions with bounded total variation.
On the relaxation of an optimal design problem for plates
Authors: Muñoz Julio , Pedregal Pablo
Published: December 2024

A general approach to relaxation for an optimal design problem for plates is proposed. Generalized minimizers in terms of Young measures are found and an attempt to reduce the design variables needed for the description of these minimizers is pursued. We examine special representations of the convex hull of a particular curve in three space dimensions where its specific properties are exploited in a fundamental way in order to obtain different descriptions of generalized minimizers. We also find the optimal relaxation by further analyzing the features of that curve.
Effective behavior of clusters of microscopic cracks inside a homogeneous conductor
Authors: Bryan Kurt , Vogelius Michael
Published: December 2024

We study the effective behaviour of a periodic array of microscopic cracks inside a homogeneous conductor. Special emphasis is placed on a rigorous study of the case in which the corresponding effective conductivity becomes nearly singular – due to the fact that adjacent cracks nearly touch. It is heuristically shown how thin clusters of such extremely close cracks may macroscopically appear as a single crack. These results have implications for our earlier work on impedance imaging.
Asymptotics of spectrum and eigenfunctions for nonselfadjoint operators generated by radial nonhomogeneous damped wave equations
Authors: Shubov Marianna A.
Published: December 2024

We consider an infinite sequence of radial wave equations obtained by the separation of variables in the spherical coordiantes from the 3‐dimensional damped wave equation with spacially nonhomogeneous spherically symmetric coefficients. The nonconservative boundary conditions are given on the sphere $|x|=a$ . Our main objects of interest are the nonselfadjoint operators in the energy space of 2‐component initial data, which are the dynamics generators for the systems governed by the aforementioned equations and boundary conditions. Our main results are precise asymptotic formulas for the complex eigenvalues and eigenfunctions of these operators and the corresponding nonselfadjoint quadratic operator pencils. Based on the asymptotic results of the present work, we will show in a forthcoming paper that the sets of root vectors of the above operators and of the dynamics generator corresponding to the full 3‐dimensional damped wave equation form Riesz bases in the appropriate energy spaces. Therefore, we will show that all these operators are spectral in the sense of Dunford.
Nonlinear multiparameter Sturm–Liouville problems
Authors: Shibata Tetsutaro
Published: December 2024

An asymptotic formula of variational eigenvalues of nonlinear multiparameter Sturm–Liouville problems is established. The proof is based on Ljusternik–Schnirelman theory on general level sets due to Zeidler, Pohozaev‐type equality and ODE techniques.
On global existence and asymptotic stability of solutions of mildly degenerate dissipative nonlinear wave equations of Kirchhoff type
Authors: Ono Kosuke
Published: December 2024

We consider the global existence and asymptotic stability of solutions to the Cauchy problem for degenerate nonlinear wave equations of Kirchhoff type with a dissipative term in unbounded domain. We derive the sharp decay estimates of the solution and its derivatives. Moreover, we show that the solution has a lower decay estimate of some algebraic rate.
Travelling waves for KdV and Boussinesq’s system revisited
Authors: Frank Leonid S.
Published: December 2024

A simple method is presented for explicitly finding the solitons’ wavetrain $\eta$ for the Korteweg–de Vries equation in terms of the wave numbers of the solitons, their number $N$ being fully determined by the initial disturbance $\eta_0 \in L_{1/2} ({\NBbbR})$ . The Boussinesq system is asymptotically examined and explicit formulae are given for the slightly deformed corresponding oscillating waves, the small parameter being $\varepsilon = h_0$ , where $h_0$ is the dimonsionless depth of the water layer at rest. The existence of such oscillatory waves is rigorously proved for the Boussinesq system. A different Boussinesq system, yielding solitons, is also revisited.
Arbitrary $n$‐vortex self‐duality solutions to the Ginzburg–Landau equations satisfying normal state conditions at infinity
Authors: Almog Y.
Published: December 2024

It is well known that, when the Ginzburg–Landau parameter $\kappa=1/\sqrt{2}$ , the second‐order Ginzburg–Landau equations may be reduced to the first‐order Bogomolnyi equations. It is established in this critical case that, for any given set of vortex locations and orders, these equations possess a unique solution which tends to the purely superconducting state at infinity. In the present contribution we focus on cases in which normal state conditions at infinity are imposed. It is found that, for any given set of vortex locations and orders, an infinite number of solutions satisfying such conditions at infinity exist.
Convergence to stationary states of solutions of the transient drift diffusion equations for semiconductor devices with prescribed currents
Authors: Jochmann Frank
Published: December 2024

The transient drift diffusion equations describing the charge transport in semiconductors coupled with Maxwell’s equations are considered. The asymptotic behavior of the solutions is investigated. In particular it is shown that they converge for $t\rightarrow\infty$ to solutions of the stationary drift diffusion equations provided that the currents corresponding to the stationary states are sufficiently small.
Dispersive effects for nonlinear geometrical optics with rectification
Authors: Lannes David
Published: December 2024

Oscillating approximate solutions to nonlinear hyperbolic dispersive systems are studied. Ansatz of three scales are used in order to deal with diffractive effects. The scaling of the approximate solutions is chosen so that diffractive, dispersive effects and rectification are present in the leading term.

The propagation along the rays of geometrical optics of the oscillating Fourier coefficients of the leading terms is corrected by a Schrödinger dispersion which appears for long times only. The propagation of the nonoscillating Fourier coefficient depends on the properties of a symmetric hyperbolic system, whose characteristic variety is the tangent cone at $0$ to the characteristic variety of the initial operator.

Equations determining the leading term require a sublinear growth condition for the corrector and the inroduction of the analytical “average operators” which convey this sublinear growth condition in a simple way and sort the nonlinearities out.

In the last part, detailed physical examples are given.
Long‐time behaviour of diffusion waves for a viscous system of conservation laws in $\mathbf{R}^N$
Authors: Escobedo Miguel , Zuazua Enrique
Published: December 2024

We consider a system of two viscous conservation laws in several space dimensions. The equations are weakly coupled so that the inviscid part of the system is not necessarily strictly hyperbolic. We analyze the long‐time behaviour of integrable non‐negative solutions. More precisely, we are interested by the profile of the first non‐trivial term of the asymptotic expansion of the solutions. The flux function may fail to be $C^2$ , thus linearization around the zero solution does not apply. We use scaling techniques. Inspired in our previous works on scalar equations we exhibit two different types of behaviour: weakly nonlinear and self‐similar.
Limit behaviour of solutions to certain kinds of boundary value problems with equivalued surface
Authors: Ta‐tsien Li , (Li Da‐qian)  , Jinhai Yan
Published: December 2024

This paper deals with the limit behaviour of solutions to certain kinds of boundary value problems with equivalued surface on a domain with thin layer. Some applications are given in resistivity well‐logging, etc.
Asymptotic Navier–Stokes equations in a thin moving boundary domain
Authors: Bayada Guy , Chambat Michèle , Ciuperca Ionel
Published: December 2024

We consider a fluid flow in a thin domain with moving boundary. Using a rescaling of the domain in time and in height, we obtain the generalized Reynolds equation for the limit pressure.
Elliptic approximations of prescribed mean curvature surfaces in Finsler geometry
Authors: Bellettini Giovanni , Fragalà Ilaria
Published: December 2024

We approximate a hypersurface $\varSigma$ with prescribed anisotropic mean curvature with solutions $u _{\varepsilon}$ of suitable nonlinear elliptic equations depending on a small parameter $\varepsilon>0$ . We work in relative geometry, by endowing $\mathbb{R}^N$ with a Finsler norm $\phi$ describing the anisotropy. The main result states that $\varSigma$ and $\{u _{\varepsilon}=0\}$ are close of order $\varepsilon^2\vert\log\varepsilon\vert^2$ , and this estimate is optimal. This is obtained for two different elliptic equations by sub‐ and supersolutions technique, under smoothness and nondegeneracy assumptions on $\varSigma$ . Basic steps are: (i) an explicit computation of the second variation of the $\phi$ ‐Minkowski content along geodesics; (ii) the definition of a Laplace–Beltrami operator on $\varSigma$ ; (iii) the expansion of the $\phi$ ‐mean curvature of $\varSigma$ in a suitable tubular neighbourhood.
Limit behaviour of solutions to a class of boundary value problem with equivalued surface for hyperbolic equations[1]This work was supported by NSFC (19871048) and NSF of Shandong province.
Authors: Li Feng‐Quan
Published: December 2024

In this paper, in the case that the equivalued surface boundary $\tilde{\varGamma}_1^\varepsilon$ shrinks to a fixed point on boundary $\varGamma_1$ , we discuss the limit behaviour of solutions for a class of boundary value problems with equivalued surface for hyperbolic equations.
Complex WKB method for 3‐level scattering systems
Authors: Joye Alain , Pfister Charles‐Edouard
Published: December 2024

In this note the $S$ ‐matrix naturally associated with a singularly perturbed three‐dimensional system of linear differential equations without turning point on the real axis is considered. It is shown that for a fairly large class of examples, the Complex WKB method gives results far better than what is proven under generic circumstances. In particular, we show how to compute asymptotically all exponentially small off‐diagonal elements of the corresponding $S$ ‐matrix.
A result on the decay of the boundary layers in the homogenization theory
Authors: Neuss‐Radu Maria
Published: December 2024

Boundary layers are used in the homogenization of elliptic problems with periodically oscillating coefficients, for example when we want to improve the macroscopic approximation given by homogenization in the neighborhood of the boundary of a domain. For problems with a special geometry the boundary layers are defined on a semi‐infinite strip $]0,1[^{n-1}\times]0,\infty[\,$ , and their energies decrease exponentially with respect to the second variable.

In our paper, we show that in general this decay property does not hold, i.e., we cannot get uniform exponential decay of the boundary layers.
Approximation de Born–Oppenheimer de sections efficaces totales diatomiques
Authors: Jecko Th.
Published: December 2024

[fr] Pour des molécules diatomiques dans la limite de Born–Oppenheimer, on construit une approximation adiabatique de plusieurs sections efficaces totales, y compris des sections inélastiques. On montre la prépondérance de la diffusion élastique et l’on en donne des termes dominants. L’un d’eux contient un potentiel effectif, ce qui permet de réduire la diffusion à celle d’un système à deux corps. De plus, l’approximation améliore une borne a priori sur d’autres sections totales.

Abstract. In the Born–Oppenheimer limit, for diatomic molecules, we approximate several total cross‐sections, including inelastic ones, by adiabatic equivalents. We show the preponderance of the elastic total cross‐section and we give leading terms for it. One of them contains a two‐body efficient potential so that the scattering behaviour may be well‐approximated by those of some two‐body system. Furthermore, the adiabatic approximation improves an a priori bound on some other total cross‐sections.
Formes normales semi‐classiques des systèmes complètement intégrables au voisinage d'un point critique de l'application moment
Authors: Vũ Ngoc San
Published: December 2024

The semi‐classical study of a 1‐dimensional Schrödinger operator near a non‐degenerate maximum of the potential has lead Colin de Verdière and Parisse to prove a microlocal normal form theorem for any 1‐dimensional pseudo‐differential operator with the same kind of singularity. We present here a generalization of this result to pseudo‐differential integrable systems of any finite degree of freedom with a Morse singularity. Our results are based upon Eliasson's classical mechanical study of critical integrable systems.
On the existence of transition layers of spike type in reaction–diffusion–convection equations
Authors: Schneider Klaus R. , Vasil'eva Adelaida B.
Published: December 2024

We investigate steady state solutions to a class of systems of reaction–diffusion–convection equations with small diffusion and small convection in case of a scalar spatial variable. Our main concern is to prove the existence of a solution with an interior layer of spike type for higher order systems without taking into consideration the influence of boundary conditions. To this end we combine two methods of the theory of singular perturbations: the method of integral manifolds and the method of boundary layer functions.
Weak asymptotic decay for a wave equation with gradient dependent damping
Authors: Vancostenoble J.
Published: December 2024

We study the problem of asymptotic behavior as t→+∞ of solutions of the weakly damped wave equation utt−Δu=−a(x)β(ut,∇u) in Ω, u=0 on ∂Ω, where Ω is a bounded, open, connected set in RN, N≥1, with smooth boundary and where λ=(λ1,…,λN+1)→β(λ1,…,λN+1) satisfies the basic assumption ∀λ, λ1β(λ)≥0. We prove the weak asymptotic stabilization in H10(Ω)×L2(Ω) of all global solutions under very weak assumptions on β (in so far as we need neither hypothesis of monotonicity on β nor condition restricting its asymptotic growth at infinity). In particular, we generalize an earlier result of M. Slemrod. Moreover the method also applies to other equations and above all to other feedbacks (boundary or pointwise feedbacks) and even to hybrid systems.
A particular type of summability of divergent power series, with an application to difference equations
Authors: Immink G.K.
Published: December 2024

We define a “weak Borel‐sum” for a class of formal power series. This is a generalization of the ordinary Borel‐sum with applications in the theory of locally analytic difference equations. We explain its relation to a particular type of accelero‐sum obtained by the use of a weak acceleration operator, and briefly discuss a corresponding Stokes phenomenon. Most results of this paper are based on the quasi‐analyticity of a certain type of Borel transform.
Complete asymptotics for shallow shells
Authors: Andreoiu Georgiana , Faou Erwan
Published: December 2024

In this paper we study the asymptotics of the three‐dimensional displacement field for clamped and free linear elastic shallow shells as the thickness tends to zero. As in the case of plates, the asymptotics contains regular terms and boundary layers. The two‐dimensional generators of the regular parts are solutions of two‐dimensional problems governed by an elliptic system in the sense of S. Agmon, A. Douglis and L. Nirenberg. This asymptotics is justified by optimal error estimates and improves the results obtained by S. Busse, P.G. Ciarlet and B. Miara.
Optimal conditions of convergence and effects of anisotropy in the homogenization of non‐uniformly elliptic problems
Authors: Briane Marc
Published: December 2024

This paper is devoted to the homogenization of the problem −div(aε∇uε)+ν uε=f in a bounded domain Ω of Rd, with Neumann's (ν=1) or Dirichlet's (ν=0) boundary conditions. The conductivity matrix aε is defined by $a_{\varepsilon }(x):=A_{\varepsilon }(\tfrac{x}{\varepsilon })$ where (Aε)ε>0 is a sequence of bounded but non‐uniformly elliptic periodic matrix‐valued functions.

We make a general assumption on Aε for that the sequence uε strongly converges in L2(Ω) to a function u0 solution of a similar problem. We also yield an example in which the compactness result holds true although the sequence Aε uniformly looses its ellipticity as ε tends to zero. Finally we illustrate the optimality of our condition on Aε in the framework of isolating thin layers.
Asymptotic and numerical analysis for unilateral contact problem with Coulomb's friction between an elastic body and a thin elastic soft layer
Authors: Bayada G. , Lhalouani K.
Published: December 2024

On étudie le comportement asymptotique d'une structure à 3 corps constituée d'une couche mince élastique placée entre un corps rigide et un corps élastique. On suppose que le contact entre les deux corps élastique est un contact unilatéral avec frottement de Coulomb non local et que les coefficients de Lamé de la couche mince dépendent de son épaisseur ε. On montre que lorsque l'épaisseur du joint tend vers zéro la structure initiale peut être remplacée par une structure à deux corps avec de nouvelles conditions à l'interface. Enfin, on présente quelques simulations numériques permettant de mettre en évidence les résultats obtenus théoriquement.
Error estimates between the linearized three‐dimensional shell equations and Naghdi's model
Authors: Lods Véronique , Mardare Cristinel
Published: December 2024

We estimate the difference between the solutions of the three‐dimensional model and the two‐dimensional Naghdi model for a thin shell. This estimation, which depends on the thickness of the shell, is obtained under the assumption that the shell is clamped along its entire lateral face.
The asymptotic behaviour of quasi‐Newtonian flow through a very thin or a very long curved pipe
Authors: Marušić Sanja
Published: December 2024

We consider an injection of incompressible viscous quasi‐Newtonian fluid in a curved pipe with a smooth central curve γ. Starting from the Navier–Stokes system with shear‐dependent viscosity, used to describe the polymeric flow or the blood flow, the 1‐dimensional model was obtained via singular perturbation as ε, the ratio between cross section area and the length of the pipe, tends to 0. The method of two‐scale convergence was applied. The limit depends only on the tangential injection along γ and the velocity, as well as the pressure drop have the tangential direction.
Homogenization of optimal control problems in variable domains. Principle of the fictitious homogenization
Authors: Kogut P. , Leugering G.
Published: December 2024

We consider the optimal control problems for the linear elliptic equations in perforated domains. Each components of mathematical description of such optimal control problem depends on small parameter ε. Problems of this type appear in sensitivity analysis, perturbation theory, and homogenization of heterogenous material. We study the problem of passing to the limit within the framework of variational S‐convergence. We derive conditions under which the so‐called fictitious limiting optimal control problem can be made explicit.
Asymptotic developments of analytic functions in cones
Authors: Meana Jorge Jiménez
Published: December 2024

In this paper we give a definition of asymptotic development of an analytic function of several complex variables. So far, there existed two different definitions which are joined by the definition given in this paper. This definition generalizes, in a natural sense, the one given for one variable. The generalization is made by changing the object polysector by a conoidal domain which is more general because all the polysectors are conoidal domains but not all the conoidal domains are polysectors.

It is given a characterization of the analytic functions that admit asymptotic developments in a cone as those which restricted to a closed subcone admit an extension of class 𝒞∞. It is proven that, through this definition, the asymptotic developments of analytic functions of several variables verify all the good properties of the asymptotic developments of analytic functions of one variable.
High‐frequency asymptotic analysis of a dissipative transmission problem resulting in generalized impedance boundary conditions
Authors: Antoine X. , Barucq H. , Vernhet L.
Published: December 2024

The present work investigates boundary conditions that modelize the penetration of a time‐harmonic wave into a dissipative obstacle. The exact model is given through a transmission problem that couples the propagations into an absorbing domain and an exterior domain. The conditions arise from an asymptotic analysis of the interior solution whose propagation is studied by using pseudodifferential technics classically involved for the construction of radiation boundary conditions. Herein, first and second‐order conditions are analyzed and some numerical experiments illustrate their validity domain.
A complex WKB method for adiabatic problems
Authors: Fedotov Alexander , Klopp Frédéric
Published: December 2024

This work is devoted to a new version of the complex WKB method suited for adiabatic perturbations of one‐dimensional periodic Schrödinger operators. Therefore, we introduce an additional parameter, and it is this parameter (and not the variable of the equation) that will become complex. This naturally leads to canonical domains where we construct solutions of the Schrödinger equation with a standard asymptotic behavior. These can be used to compute the asymptotics of the exponentially small coefficients of transfer matrices (e.g., scattering matrices, monodromy matrices, etc.). We give an example of such a computation.

Résumé. Ce travail est consacré à une nouvelle version de la méthode BKW complexe adaptée à l'étude des perturbations adiabatiques d'équations de Schrödinger périodiques en dimension 1. Nous introduisons un paramètre supplémentaire; c'est ce paramètre qui sera rendu complexe (au lieu de la variable de l'équation). Ceci nous conduit de façon naturelle à la définition des domaines canoniques dans lesquels on construit des solutions aux comportements asymptotiques connus. Ces développements asymptotiques peuvent être utilisés pour contrôler l'asymptotique des coefficients exponentiellement petits de matrices de transfert (par exemple, de matrices de diffusion, de matrices de monodromie, etc.). On donne un exemple d'un tel calcul.
A probabilistic approach to the homogenization of divergence‐form operators in periodic media
Authors: Lejay Antoine
Published: December 2024

We prove here using stochastic analysis the homogenization property of second‐order divergence‐form operators with lower‐order differential terms (possibly highly‐oscillating) in periodic media. The coefficients are not assumed to have any regularity, so the stochastic calculus theory for processes associated to Dirichlet forms is used. The Girsanov theorem and the Feynman–Kac formula are used to work on the probabilistic representation of the solutions of some PDEs.
Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems
Authors: Schneider Guido , Uecker Hannes
Published: December 2024

Nonlinear coupled mode equations occur as universal modulation equations in various circumstances. It is the purpose of this paper to prove exact estimates between the approximations obtained via the nonlinear coupled mode equations and solutions of the original parabolic or hyperbolic systems. The models which we consider contain all difficulties which have to be overcome in the general case.
Blow‐up for a class of nonlinear parabolic problems
Authors: Andreu F. , Mazón J.M. , Simondon F. , Toledo J.
Published: December 2024

For nonlinear parabolic equations of the form ut=Δum−uμ‖∇um‖q+up, we prove nonexistence of global admissible solutions for large initial data for some range of the parameters m, μ, q and p. To do so we use comparison with suitable blowing up self‐similar subsolutions. We also prove that for the complementary range of the parameters for which we obtain blow‐up, there exists globally bounded admissible solutions.
Weakly coupled dynamical systems and applications
Authors: Carrive M. , Miranville A. , Piétrus A. , Rakotoson J.M.
Published: December 2024

In this article, we define a new class of dynamical systems that are not associated with semigroups and that we call weakly coupled systems (in the sense that the initial conditions for the different components of the system are not independent) and study the asymptotic behavior of such systems. In particular, we define and study the notions of global attractor, inertial manifold and exponential attractor associated with a weakly coupled system. We also consider the nonautonomous case. As an example, we study the asymptotic behavior of weakly coupled Cahn–Hilliard equations.
A justification of linear Koiter and Naghdi's models for totally clamped shell
Authors: Lods Véronique , Mardare Cristinel
Published: December 2024

We consider a shell, i.e., a three‐dimensional body with a small thickness (denoted by 2ε), which is clamped along its entire lateral boundary and subjected to regular loads. In the linear case, one can use the two‐dimensional models of Koiter or Naghdi to calculate the displacement vector field of the shell. Some error estimates have been obtained in [12,13] between these models and the three‐dimensional displacement for flexural or membrane shells. Here, we do not make any assumptions on the geometry of the shell. In particular, the space of inextensional displacements can be reduced to zero. The assumptions on the loads are weak: for the sake of simplicity, one can consider regular loads (in H1) which do not depend on the transverse variable. We then establish a relative error estimate for the scaled linearized deformation tensor between Koiter's model (or Naghdi's model) and the three‐dimensional model. These estimates hold though the limit model is not always known. In addition, further assumptions on the data allow to recover the error estimates concerning the displacements which have been proved in [12,13].
Calculation of Stokes multipliers by analytic equivalence
Authors: Schmidt D. , Sibuya Y. , Tabara T.J.
Published: December 2024

We have demonstrated previously how to calculate a Stokes multiplier concerning subdominant solutions of a second order differential equation with polynomial coefficients without utilizing any suitable integral representation of its solutions. With a recent discovery of a transformation, we can derive a new Stokes multiplier from the previously calculated multiplier.
Riemannian approximation of Finsler metrics
Authors: Braides Andrea , Buttazzo Giuseppe , Fragalà Ilaria
Published: December 2024

We show that the class of smooth and isotropic Riemannian metrics is dense in the class of all lower semicontinuous Finsler metrics, with respect to the Γ‐convergence of energy integrals.
Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics
Authors: Berthelin F. , Bouchut F.
Published: December 2024

We obtain rigorously the correspondence between kinetic and macroscopic invariant domains for a vector kinetic BGK system considered in a previous paper of the authors. We establish the convergence, as the relaxation parameter tends to 0, to weak entropy solutions of isentropic gas dynamics equations.
Resolvent estimates for the Dirac operator in weighted Sobolev spaces
Authors: Pladdy Christopher
Published: December 2024

We consider the Dirac operator with a scalar short‐range potential. Estimates for the extended resolvents, R±(λ), of this operator considered as a bounded operator from ℒs2 into the weighted Sobolev space ℋ−s1 are discussed. The extended resolvents R0±(λ) of the free Dirac operator are shown to be O(λ) as |λ|→∞ in the uniform operator topology of B(ℒs2,ℋ−s1), and this is shown to be the optimum result. R±(λ) are shown to be R0±(λ)+O(1) as |λ|→∞ in B(ℒs2,ℋ−s1). R±(λ)−R0±(λ) are shown to converge strongly to zero in B(ℒs2,ℋ−s1). The method of proof uses results for the free Schrödinger operator resolvent and the free Dirac operator resolvent, both considered as operators from ℒs2 to ℋ−s1, and the estimates for the free Dirac and Schrödinger resolvents, both considered as operators from ℒs2 to ℒ−s2.
Persistency of 2D perturbations of one‐dimensional solutions for a Cahn–Hilliard flow model under high shear
Authors: Boyer Franck , Fabrie Pierre
Published: December 2024

We consider a diphasic system in a high shear regime when separation of phases occurs. One can observe that the two phases organize themselves into numerous bands, parallel to the flow direction. Mathematically, these are solutions of a certain system of equations depending only upon the transversal variable (1D solutions). We study the stability of these 1D solutions with respect to 2D perturbations. The mathematical model used in our analysis is a coupling between a Cahn–Hilliard equation and the Navier–Stokes equations in two dimensions. We show that a small 2D perturbation of a given 1D solution persists for significant times. We give the precise size of such a perturbation and its time of persistence. Moreover, we obtain an asymptotic expansion of the solution in the considered cases. Note that, for a mathematical model to be realistic one has to take into account the fact that in experiments the high shear regime is obtained in elongated domains (a very thin Couette cell for example). Therefore, we perform the mathematical analysis of this problem in a stretched domain.
Asymptotic derivation of a Navier condition for the primitive equations
Authors: Bresch D. , Guillén‐González F. , Masmoudi N. , Rodríguez‐Bellido M.A.
Published: December 2024

This paper is devoted to the establishment of a friction boundary condition associated with the hydrostatic Navier–Stokes equations (also called the primitive equations). Usually the Navier boundary condition is used, as a wall law, for a fluid governed by the Navier–Stokes equations when we want to modelize roughness. We consider here an anisotropic Navier boundary condition corresponding to the anisotropic Navier–Stokes equations. By an asymptotic analysis with respect to the aspect ratio of the domain, we obtain a friction boundary condition for the limit system, that is the primitive equations.

This asymptotic boundary condition only concerns the trace of the horizontal components of the velocity field and the trace of its vertical derivative.
Aharonov–Bohm effect in scattering by a chain of point‐like magnetic fields
Authors: Ito Hiroshi T. , Tamura Hideo
Published: December 2024

According to the Aharonov–Bohm effect, magnetic potentials have a direct significance to the motion of particles in quantum mechanics. We study this quantum effect through the scattering by several point‐like magnetic fields at large separation in two dimensions. We derive the asymptotic formula for scattering amplitudes as the distances between centers of fields go to infinity. The result heavily depends on the location of centers. A special emphasis is placed on the case of scattering by fields with centers on an even line. The obtained formula depends on fluxes of fields and on ratios of distances between adjacent centers. We figure the approximate values of differential cross sections to see how the pattern of interferences changes with flux parameters.
Well‐posedness for parabolic equations of arbitrary order
Authors: Marchi Claudio
Published: December 2024

This paper deals with the well‐posedness of the Cauchy problem for higher order parabolic equations. Our aim is to show existence and uniqueness of the solution belonging to a suitable weighted Sobolev space, provided that the weight function satisfies some appropriate differential inequality (the “dual” one). Under some restrictions on the growth of the coefficients as |x|→∞ (see conditions (A1)–(A4) below), we obtain a simplified dual inequality; we deduce a well‐posedness result which extends results known in literature. In Appendix, dropping any growth condition on the coefficients, we extend our result, but the dual inequality is complicated.
Inverse scattering for Stark Hamiltonians with short‐range potentials
Authors: Nicoleau François
Published: December 2024

We consider the Stark Hamiltonian H=½p2−x1+V(x) which describes the scattering of a quantum mechanical particle in $\mathbb{R}^{n}$ by a short‐range potential in the presence of a constant electric field. We show that the electric potential V is uniquely determined by the high energy limit of the scattering operator, if the dimension n≥3. We prove our results using the Enss–Weder time‐dependent method.
Asymptotic separation of the spectrum of quadratic operator pencils associated with damped dynamical systems
Authors: Pivovarchik Vjacheslav , Tretter Christiane
Published: December 2024

We investigate the spectrum of a damped quadratic operator pencil with 2×2 block operator matrix coefficients. Our main result is that the spectrum splits asymptotically into four branches of eigenvalues and we determine their asymptotic behaviour. An application to the vibrations of two interacting connected strings and beams is given where one of them is damped.
Asymptotic analysis of dynamic problem for linearly elastic generalized membrane shells
Authors: Ji Ye
Published: December 2024

We consider a dynamic linearly elastic generalized membrane shell with variable thickness and show that the solutions of the three‐dimensional equations, as the thickness of the shell goes to zero, converge to the solution of the two‐dimensional dynamic generalized membrane shell.
Multi‐peak solutions for a class of degenerate elliptic equations
Authors: Giacomini Alessandro , Squassina Marco
Published: December 2024

By means of a penalization argument due to del Pino and Felmer, we prove the existence of multi‐spike solutions for a class of quasilinear elliptic equations under natural growth conditions. Compared with the semilinear case some difficulties arise, mainly concerning the properties of the limit equation. The study of concentration of the solutions requires a somewhat involved analysis in which a Pucci–Serrin type identity plays an important role.
On internal and boundary layers with unbounded energy in thin shell theory. Elliptic case
Authors: Sanchez‐Palencia E.
Published: December 2024

We consider the system of equations of Koiter thin shell theory in a slightly simplified form, in the case when the limit (for small thickness) problem is elliptic, i.e., the principal curvatures of the middle surface are everywhere of the same sign. Under singular loadings, which are not in the dual of the energy space of the limit problem, the energy of the solutions grows without limit as the thickness tends to zero. Moreover, it concentrates on boundary layers along the singularities of the loading. We define and prove the convergence to the leading order term in that layers.
L2‐convergence results for linear dissipative wave equations in unbounded domains
Authors: Ikehata Ryo
Published: December 2024

Hyperbolic linear Cauchy problem εu″+Au+u′=0, u(0)=u0, u′(0)=u1, with “nonnegative” selfadjoint operator A in a real Hilbert space H is first considered. It is shown that the solution uε tends to some solution v as ε↓0 for the parabolic equation v′+Av=0 in a certain sense. Some applications are given. Finally, we present hyperbolic‐hyperbolic convergence results such as the solution for the damped wave equations goes to some solution for the free wave equations as the effect of the damping vanishes in a concrete context.
Homogenization of degenerate elliptic‐parabolic equations
Authors: Paronetto Fabio
Published: December 2024

In this paper we give a result of G‐convergence for a class of strongly degenerate parabolic equations in the case of periodic coefficients. The operators have the form μ(x)∂t−div(a(x,t)·D) where the quadratic form associated to a(x,t) is degenerating as a Muckenhoupt weight and the coefficient μ is greater or equal to zero, possibly μ≡0, that is the operator may be elliptic, parabolic or elliptic‐parabolic.
Radionuclide transport model with wells
Authors: Choquet Catherine
Published: December 2024

We consider a model describing compressible flow and transport processes of nuclear contaminants in porous media. The transport of radionuclides and heat is described by a nonlinear coupled parabolic system. The temperature equation is of degenerate parabolic type. We model the wells using measures as source terms.
Estimates for Fourier transforms of surface‐carried densities on surfaces with singular points
Authors: Liess Otto
Published: December 2024

We study decay estimates for Fourier transforms of smooth densities defined on surfaces with uniplanar singularities.
New effects in propagation of waves for reaction–diffusion systems
Authors: Vakulenko S. , Volpert V.
Published: December 2024

The Cauchy problem for reaction–diffusion systems is studied. A notion of generalized travelling waves (GTW) is introduced to describe the large time behavior of solutions, in particular for the case of a nonhomogeneous medium. If the nonhomogeneous perturbation is asymptotically small, existence and stability of GTW is proved and their velocity is found. If the unperturbed systems is decoupled, the behavior of GTW for the perturbed system can be periodic or even chaotic both for homogeneous and nonhomogeneous perturbations. Dispersion of GTW on nonhomogeneities and applications to combustion problems are discussed.
Optimal bounds for the inviscid limit of Navier–Stokes equations
Authors: Abidi H. , Danchin R.
Published: December 2024

We consider the inviscid limit of incompressible two‐dimensional fluids with initial vorticity in L∞ and in some Besov space Bη2,∞ with low regularity index. We obtain a general result of strong convergence in L2 which applies to the case of vortex patches with smooth boundaries. The rate of convergence we find is (νt)3/4 (where ν stands for the viscosity and t, for the time). It improves the (νt)1/2 rate given by P. Constantin and J. Wu in (Nonlinearity 8 (1995), 735–742). Besides, it is shown to be optimal in the case of circular vortex patches.
Existence and finite‐time blow‐up for the solution to a thin‐film surface evolution problem
Authors: Boutat M. , D'Angelo Y. , Hilout S. , Lods V.
Published: December 2024

The aim of this paper is to study the evolution of the surface of a crystal structure, constituted by a linearly elastic substrate and a thin film. After appropriate scalings, a formal asymptotical expansion of the displacement, under some assumptions, yields the following nonlinear PDE [Formula: see text] where θ is a coefficient related to the crystal, and h(t,x) describes the spatial evolution of the film surface. We give here some results about the finite‐time blow‐up and prove the existence and uniqueness of a solution in L2(0,t*;Hper4(0,1))∩L∞(0,t*;Hper2(0,1)). We also present some numerical computations confirming the blow‐up scenario.
Résonances en dimension un pour l'opérateur de Schrödinger
Authors: Servat E.
Published: December 2024

On s'intéresse à l'existence et à la localisation des résonances pour l'opérateur de Schrödinger semi‐classique unidimensionnel, dans le cas de puits multiple dans une île. On obtient en particulier une condition géométrique pour la transition entre le croisement et l'anti‐croisement des résonances dans le cas de deux puits de potentiel.
A 3D–1D Young measure theory of an elastic string
Authors: Freddi Lorenzo , Paroni Roberto
Published: December 2024

A variational limit defined on the space of one‐dimensional Young measures is obtained from three‐dimensional elasticity via dimension reduction. The physical requirement that the energy becomes infinite when the volume locally vanishes is taken into account. The rate at which it blows up characterizes the domain of the limit energy. The obtained limit problem uniquely determines the energy density of the elastic string.
Global existence and asymptotic behaviour for a mildly degenerate dissipative hyperbolic equation of Kirchhoff type
Authors: Ghisi Marina , Gobbino Massimo
Published: December 2024

We investigate the evolution problem

u"+δu'+m(|A1/2u|2)Au=0,

u(0)=u0,  u'(0)=u1,

where H is a Hilbert space, A is a self‐adjoint non‐negative operator on H with domain D(A), δ>0 is a parameter, and m :[0,+∞[→[0,+∞[ is a locally Lipschitz continuous function. We prove that this problem has a unique global solution for positive times, provided that the initial data (u0,u1)∈D(A)×D(A1/2) satisfy a suitable smallness assumption and the non‐degeneracy condition m(|A1/2u0|2)>0. Moreover (u(t),u′(t),u″(t))→(u∞,0,0) in D(A)×D(A1/2)×H as t→+∞, where |A1/2u∞|m(|A1/2u∞|2)=0. These results apply to degenerate hyperbolic PDEs with non‐local non‐linearities.
Asymptotic analysis of quantum scattering under mesoscopic scaling
Authors: Benedetto D. , Esposito R. , Pulvirenti M.
Published: December 2024

We consider a quantum particle scattered by an obstacle localized around the origin. We look at the time evolution in a large space‐time scale, O(ε−1), assuming as initial datum a suitable WKB state with an amplitude varying on scale ε−1. We study asymptotic behavior of the solution when ε vanishes. Our analysis is complementary to the one performed by Nier (Transport Theory Statist. Phys. 24(4–5) (1995), 591–629; Ann. Sci. École Norm. Sup. (4) 29 (1996), 149–183) who studied the same problem directly in terms of the Wigner formalism.
About MHD system with small parameter
Authors: Benameur J. , Ghazel M. , Majdoub M.
Published: December 2024

In this paper, we study the convergence of strong solutions of a MHD system. The proofs, in booth cases of ${\mathbb{T}}^{3}$ or ${\mathbb{R}}^{3}$ , are based on spectral properties of the penalized operator and the energy method. Moreover, in the case of the whole space, we prove a refined convergence result for initial data 2D + 3D.
Non‐local interactions in the homogenization closure of thermoelectric functionals
Authors: Camar‐Eddine M. , Milton G.W.
Published: December 2024

It is a very well‐known fact that the effective properties of a heterogeneous electrical medium may contain a non‐local term. The same phenomenon can occur within a heterogeneous thermally conducting medium. We are interested in the set of all non‐local interactions which may arise from the homogenization of a thermoelectric medium where there are couplings between the temperature and the electric field. We consider a bounded open subset Ω⊂ $\mathbb{R}^{3}$ and we show that any non‐local energy of the kind

F(u,v)=∫Ω×Ω $\pmatrix{u(x)-u(y)\cr v(x)-v(y)\cr}$ ·μ(dx,dy) $\pmatrix{u(x)-u(y)\cr v(x)-v(y)\cr}$ ,

belongs to the closure of the set of thermoelectric functionals, provided that the positive definite symmetric matrix‐valued measure μ(dx,dy) makes this energy functional continuous in the strong topology of L2(Ω, $\mathbb{R}^{2}$ ).
Rate of convergence in the Fourier inversion of indicator functions
Authors: González Vieli Francisco Javier
Published: December 2024

The rate of convergence, at a point x, of the Fourier integral of the indicator function of a regular plane domain U has been investigated by Popov [Russian Math. Surveys 52 (1997), 73–145] and by Pinsky and Taylor [J. Fourier Anal. Appl. 3 (1997), 647–703] for x not on the boundary $\curpartial U$ of U; they have shown that the larger the maximal order of contact of $\curpartial U$ with the circles centered at x, the slower the convergence. We show here that Popov's approach, which uses the method of stationary phase, can be extended to the case x on the boundary $\curpartial U$ , giving exactly the same relation between rate of convergence and maximal order of contact.
Convergence of compressible Euler–Poisson equations to incompressible type Euler equations
Authors: Peng Yue‐Jun , Wang Ya‐Guang
Published: December 2024

In this paper, we study the convergence of time‐dependent Euler–Poisson equations to incompressible type Euler equations via the quasi‐neutral limit. The local existence of smooth solutions to the limit equations is proved by an iterative scheme. The method of asymptotic expansion and the symmetric hyperbolic property of the systems are used to justify the convergence of the limit.
Long‐time asymptotics via entropy methods for diffusion dominated equations
Authors: Carrillo José A. , Fellner Klemens
Published: December 2024

Uniform convergence rates of diffusion dominated equations towards their asymptotic profiles are quantified via entropy methods for bounded integrable non‐negative initial data with finite entropy. Convergence rates are sharp since they coincide with the purely diffusive ones. The approach is applied to both convection– and absorption–diffusion equations. Finally, Wasserstein metrics are used to control the expansion of the support for the convection–diffusion case.
Homogenization of forward‐backward parabolic equations
Authors: Amar M. , Dall'Aglio A. , Paronetto F.
Published: December 2024

We study the homogenization of the equation [Formula: see text] where R is a periodic function which may vanish or change sign, with appropriate initial/final conditions. The main tool is a compactness result for sequences of functions which have bounded norms in the spaces associated to the problems.