approximate maximum likelihood period estimation from sparse noisy timing data the problem of estimating the period of a series of periodic events is considered under the condition where the measurements of the times of occurrence are noisy and sparse the problem is common to bit synchronisation in telecommunications and pulse train parameter estimation in electronic support among other applications two new algorithms are presented which represent different compromises between computational and statistical efficiency the first extends the separable least squares line search sls2 algorithms of sidiropoulos et al having very low computational complexity while attaining good statistical accuracy the second is an approximate maximum likelihood algorithm based on a low complexity lattice search and is found to achieve excellent accuracy

decay of the navier stokes poisson equations we establish the time decay rates of the solution to the cauchy problem for the compressible navier stokes poisson system via a refined pure energy method in particular the optimal decay rates of the higher order spatial derivatives of the solution are obtained the h s 0 s 3 2 negative sobolev norms are shown to be preserved along time evolution and enhance the decay rates as a corollary we also obtain the usual lp l2 1 p 2 type of the optimal decay rates compared to the compressible navier stokes system and the compressible irrotational euler poisson system our results imply that both the dispersion effect of the electric field and the viscous dissipation contribute to enhance the decay rate of the density our proof is based on a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis

the pointwise estimates of diffusion wave of the compressible micropolar fluids abstract the pointwise estimates for the compressible micropolar fluids in dimension three are given which exhibit generalized huygens principle for the fluid density and fluid momentum as the compressible navier stokes equation while the micro rational momentum behaves like the fluid momentum of the euler equation with damping to circumvent the complexity from 7 7 green s matrix we use the decomposition of fluid part and electromagnetic part for the momentums to study three smaller green s matrices the following from this decomposition is that we have to deal with the new problem that the nonlinear terms contain nonlocal operators we solve it by using the natural match of these new green s functions and the nonlinear terms moreover to derive the different pointwise estimates for different unknown variables such that the estimate of each unknown variable is in agreement with its green s function we develop some new estimates on the nonlinear interplay between different waves

optimal time decay of the compressible micropolar fluids abstract this paper primarily studies the large time behavior of solutions to the cauchy problem on the compressible micropolar fluid system which is a generalization of the classical navier stokes system the asymptotic stability of the steady state with the strictly positive constant density the vanishing velocity and micro rotational velocity is established under small perturbation in regular sobolev space moreover it turns out that both the density and the velocity tend time asymptotically to the corresponding equilibrium state with rate 1 t 3 4 in l 2 and the micro rotational velocity also tends to the equilibrium state with the faster rate 1 t 5 4 in l 2 norm the proof is based on the spectrum analysis and time weighted energy estimate

almost periodic solutions to some semilinear non autonomous thermoelastic plate equations abstract the paper is concerned with the existence of almost periodic solutions to the so called semilinear thermoelastic plate systems for that the strategy consists of seeing these systems as a particular case of the semilinear parabolic evolution equations x t a t x t f t x t t r where a t for t r is a family of sectorial linear operators on a banach space x satisfying the so called acquistapace terreni conditions and f is a function defined on a real interpolation space x for 0 1 under some reasonable assumptions it will be shown that has a unique almost periodic solution we then make use of the previous result to obtain the existence and uniqueness of an almost periodic solution to the thermoelastic plate systems

optimal lp lq convergence rates for the compressible navier stokes equations with potential force in this paper we are concerned with the optimal lp lq convergence rates for the compressible navier stokes equations with a potential external force in the whole space under the smallness assumption on both the initial perturbation and the external force in some sobolev spaces the optimal convergence rates of the solution in lq norm with 2 q 6 and its first order derivative in l2 norm are obtained when the initial perturbation is bounded in lp with 1 p 6 5 the proof is based on the energy estimates on the solution to the nonlinear problem and some lp lq estimates on the semigroup generated by the corresponding linearized operator

a new approach to stochastic evolution equations with adapted drift abstract in this paper we develop a new approach to stochastic evolution equations with an unbounded drift a which is dependent on time and the underlying probability space in an adapted way it is well known that the semigroup approach to equations with random drift leads to adaptedness problems for the stochastic convolution term in this paper we give a new representation formula for the stochastic convolution which avoids integration of non adapted processes here we mainly consider the parabolic setting we establish connections with other solution concepts such as weak solutions the usual parabolic regularity properties are derived and we show that the new approach can be applied in the study of semilinear problems with random drift at the end of the paper the results are illustrated with two examples of stochastic heat equations with random drift

existence of weighted pseudo anti periodic solutions to some non autonomous differential equations abstract in this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti periodicity which generalize respectively the well known notions of periodicity and that of anti periodicity basic properties of these new functions are discussed furthermore the existence of weighted pseudo anti periodic solutions to some damped non autonomous second order differential equations will be investigated to illustrate our abstract results the existence of weighted pseudo anti periodic solutions to a plate like equation is discussed

massera problem for non autonomous retarded differential equations abstract in this paper under acquistapace terreni conditions we study the existence of periodic solutions for some non autonomous semilinear partial functional differential equation with delay we assume that the linear part is non densely defined the delayed part is assumed to be periodic with respect to the first argument using a fixed point theorem for multivalued mapping some sufficient conditions are given to prove the existence of periodic solutions an example is shown to illustrate our results

optimal regularity and fredholm properties of abstract parabolic operators in l p spaces on the real line we study the operator mathcal l u t u t a t u t on l p mathbb r x for sectorial operators a t with t in mathbb r on a banach space x that are asymptotically hyperbolic satisfy the acquistapace terreni conditions and have the property of maximal l p regularity we establish optimal regularity on the time interval mathbb r showing that mathcal l is closed on its minimal domain we further give conditions for ensuring that mathcal l is a semi fredholm operator the fredholm property is shown to persist under a t bounded perturbations provided they are compact or have small a t bounds we apply our results to parabolic systems and to generalized ornstein uhlenbeck operators

riccati equation arising in a boundary control problem with distributed parameters global existence is proved for the solution of a riccati differential equation connected with the synthesis of a boundary control problem governed by parabolic partial differential equations

initial boundary value problems and optimal control for nonautonomous parabolic systems a large class of linear nonautonomous parabolic systems in bounded domains is considered with control acting on the boundary through dirichlet or neumann conditions from the point of view of semigroup theory the results from rend sem mat univ padova 78 1987 pp 47 107 on fundamental solutions for abstract parabolic equations lecture notes in math vol 1223 springer verlag berlin heidelberg 1986 pp 1 11 on abstract homogeneous parabolic cauchy problems allow operators with varying domains and holder continuous coefficients to be handled a representation formula for solutions corresponding to square integrable control functions is derived and used to solve a linear quadratic regulator problem over finite time horizon by a direct study of the associated integral riccati equation

control of parabolic pdes with time varying spatial domain czochralski crystal growth process this paper considers the optimal control problem for a class of convection diffusion reaction systems modelled by partial differential equations pdes defined on time varying spatial domains the class of pdes is characterised by the presence of a time dependent convective transport term which is associated with the time evolution of the spatial domain boundary the functional analytic description of the pde yields the representation of the initial and boundary value problem as a nonautonomous parabolic evolution equation on an appropriately defined infinite dimensional function space the properties of the time varying evolution operator to guarantee existence and well posedness of the initial and boundary value problem are demonstrated which serves as the basis for the optimal control problem synthesis an industrial application of the crystal temperature regulation problem for the czochralski crystal growth process is considered and numerical simulation results are provided

global well posedness and large time decay for the 2d micropolar equations abstract this paper studies the global in time regularity and large time behavior of solutions to the 2d micropolar equations with only angular viscosity dissipation micropolar equations model a class of fluids with nonsymmetric stress tensor such as fluids consisting of particles suspended in a viscous medium when there is no kinematic viscosity in the momentum equation the global regularity problem is not easy due to the lack of suitable bounds on the derivatives the idea here is to fully exploit the structure of the system and control the vorticity via the evolution equation of a combined quantity of the vorticity and the micro rotation angular velocity to understand the large time behavior we overcome two main difficulties the lack of kinematic viscosity and the presence of linear terms classical tools such as the fourier splitting method of schonbek and kato s approach for the decay of small solutions do not apply here we introduce a diagonalization process to eliminate the linear terms and rely on the uniform bounds for the first derivatives of the solutions to generate suitable decay rates

global variational solutions to the compressible magnetohydrodynamic equations abstract we prove the existence of globally defined variational solutions to the compressible magnetohydrodynamic mhd equations with the coefficients depending on the temperature as a by product we give a simple proof for the nonexistence of nontrivial weak time periodic solutions by the entropy principle of clausius duhem and a new poincare type inequality

global existence and optimal convergence rates of solutions for 3d compressible magneto micropolar fluid equations abstract the cauchy problem for the three dimensional compressible magneto micropolar fluid equations is considered existence of global in time smooth solutions is established under the condition that the initial data are small perturbations of some given constant state moreover we obtain the time decay rates of the higher order spatial derivatives of the solution by combining the l p l q estimates for the linearized equations and the fourier splitting method if the initial perturbation is small in h 3 norm and bounded in l 1 norm

existence and uniqueness of the solution to the dissipative 2d quasi geostrophic equations in the sobolev space we study the two dimensional dissipative quasi geostrophic equations in the sobolev space open image in new window existence and uniqueness of the solution local in time is proved in h s when s 2 1 existence and uniqueness of the solution global in time is also proved in h s when s 2 1 and the initial data open image in new window is small for the case s 2 1 we also obtain the unique large global solution in h s provided that open image in new window is small enough

a regularity criterion for the 3d magneto micropolar fluid equations in triebel lizorkin spaces abstract we consider the regularity criterion for the 3d magneto micropolar fluid equations in triebel lizorkin spaces it is proved that if u l p 0 t f q 2 q 3 0 with 2 p 3 q 2 3 2 q then the solution remains smooth in 0 t as a corollary we obtain the classical beal kato majda criterion that is the condition u l 1 0 t b 0 ensures the smoothness of the solution

global existence of small solutions to a class of nonlinear evolution equations on etudie le comportement global des solutions d une classe d equations d evolution non lineaires on considere le probleme aux valeurs initiales pour des equations quasilineaires qui sont des perturbations d equations lineaires dissipatives

initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids the equations of motion of compressible viscous and heat conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region the global solution in time is proved to exist uniquely and approach the stationary state ast provided the prescribed initial data and the external force are sufficiently small

global existence and decay estimate of solutions to magneto micropolar fluid equations abstract we are concerned with magneto micropolar fluid equations 1 3 1 4 the global existence of solutions to the cauchy problem is investigated under certain conditions precisely for the magneto micropolar navier stokes mmns system we obtain global existence and large time behavior of solutions near a constant states in r 3 appealing to a refined pure energy method we first obtain a global existence theorem by assuming that the h 3 norm of the initial data is small but the higher order derivatives can be arbitrary large if the initial data belongs to homogeneous sobolev norms h s 0 s 3 2 or homogeneous besov norms b 2 s 0 s 3 2 we obtain the optimal decay rates of the solutions and its higher order derivatives as an immediate byproduct we also obtain the usual l p l 2 1 p 2 type of the decay rates without requiring that the l p norm of initial data is small at last we derive a weak solution to 1 3 1 4 in r 2 with large initial data

global regularity of 3d nonhomogeneous incompressible magneto micropolar system with the density dependent viscosity abstract this paper is concerned with the 3d nonhomogeneous incompressible magneto micropolar equations with density dependent viscosity and vacuum in smooth bounded domains we prove that the system has a unique global smooth solution under the assumption that the initial energy is suitably small

global existence and convergence rates of smooth solutions for the compressible magnetohydrodynamic equations abstract in this paper we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations in r 3 we prove the global existence of the smooth solutions by the standard energy method under the condition that the initial data are close to the constant equilibrium state in h 3 framework moreover if additionally the initial data belong to l p with 1 p 6 5 the optimal convergence rates of the solutions in l q norm with 2 q 6 and its spatial derivatives in l 2 norm are obtained

existence of weighted pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations abstract in this paper under acquistapace terreni conditions we make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of weighted pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations applications include the existence of weighted pseudo almost periodic solutions to a nonautonomous heat equation with gradient coefficients