on a local existence theorem of neumann problem for some quasilinear hyperbolic systems of 2nd order on considere l existence locale en temps des solutions pour un systeme hyperbolique quasilineaire avec des conditions aux limites de type neumann

global well posedness for the two dimensional coupled chemotaxis generalized navier stokes system with logistic growth abstract in this paper we investigate cauchy problem for the two dimensional incompressible chemotaxis navier stokes equations with the lower fractional diffusion t n u n n n c n n 2 t c u c c c n t u u u 2 u p n where 1 2 and 1 2 1 we obtain the global in time existence and uniqueness of weak solution to the equations for a class of large initial data by making use of the coupled structure of system and damping effect of the logistic source and developing the l 4 3 r 2 estimate for vorticity

global existence and large time behavior for a two dimensional chemotaxis shallow water system abstract this paper concerns the chemotaxis shallow water system in two dimensional whole spaces we first establish the global existence of strong solution under the condition that the initial data are close to the constant equilibrium state in h n r 2 n 3 framework then the optimal time decay rates of the global solution are obtained by the method of energy estimates if the initial data belong to h s r 2 0 s 1 additionally

global classical solutions in chemotaxis navier stokes system with rotational flux term the coupled chemotaxis fluid system nt n ns x n c c u n x t 0 t ct c nc u c x t 0 t ut u u u p n x t 0 t u 0 x t 0 t is considered under the no flux boundary conditions for n c and the dirichlet boundary condition for u on a bounded smooth domain rn n 2 3 0 1 we assume that s x n c is a matrix valued sensitivity under a mild assumption such that s x n c s0 c0 with some non decreasing function s0 c2 0 it contrasts with the related scalar sensitivity case that does not possess the natural gradient like functional structure associated estimates based on the natural functional seem no longer available in the present work a global classical solution is constructed under a smallness assumption on c0 l and moreover we obtain boundedness and large time convergence for the solution meaning that small initial concentration of chemical forces stabilization

decoupling elastic waves and its applications abstract in this paper we consider time harmonic elastic wave scattering governed by the lame system it is known that the elastic wave field can be decomposed into the shear and compressional parts namely the pressure and shear waves that are generally coexisting but propagating at different speeds we consider the third or fourth kind impenetrable scatterer and derive two geometric conditions respectively related to the mean and gaussian curvatures of the boundary surface of the scatterer that can ensure the decoupling of the shear and pressure waves the decoupling results are new to the literature and are of significant interest for their own sake as an interesting application we apply the decoupling results to the uniqueness and stability analysis for inverse elastic scattering problems in determining polyhedral scatterers by a minimal number of far field measurements

layer stripping for a transversely isotropic elastic medium in this paper we develop a layer stripping algorithm for transversely isotropic elastic materials in three dimensional space we first prove that by making displacement and traction measurements at the boundary of these elastic materials one can determine the elastic tensor and all its derivatives at the boundary the elastic measurements made at the boundary are encoded in the dirichlet to neumann dn map then we use the riccati equation developed in g nakamura and g uhlmann a layer stripping algorithm in elastic impedance tomography in inverse problems in wave propagation ima vol math appl 90 springer verlag new york 1997 pp 375 384 for the dn map in any anisotropic elastic medium to approximate the elastic tensor in the interior

boundedness and asymptotic behavior to a chemotaxis fluid system with singular sensitivity and logistic source abstract in this paper we consider the following chemotaxis fluid model with singular sensitivity and logistic source n t u n n n c c r n n k x t 0 c t u c c c n x t 0 u t u u u p n x t 0 u 0 x t 0 in a bounded domain r n n 2 3 with smooth boundary under the non flux boundary conditions for n and c and the non slip boundary condition for u we establish the global boundedness and the time decay rates of the classical solutions for any k 1 provided that satisfies suitable restrictions

global solvability of chemotaxis fluid systems with nonlinear diffusion and matrix valued sensitivities in three dimensions abstract in this work we extend a recent result to chemotaxis fluid systems which include matrix valued sensitivity functions s x n c 0 2 r 3 3 in addition to the porous medium type diffusion which were discussed in the previous work namely we will consider the system n t u n n m n s x n c c x t 0 c t u c c c n x t 0 u t u u u p n x t 0 u 0 x t 0 in a bounded domain r 3 with smooth boundary assuming that m 1 0 satisfy m 4 3 that the matrix valued function s x n c 0 2 r 3 3 satisfies s x n c s 0 1 n for some s 0 0 and suitably regular nonnegative initial data we show that the corresponding no flux dirichlet boundary value problem emits at least one global very weak solution upon comparison with results for the fluid free system this condition appears to be optimal moreover imposing a stronger condition for the exponents m and i e m 2 5 3 we will establish the existence of at least one global weak solution in the standard sense

how far do chemotaxis driven forces influence regularity in the navier stokes system the chemotaxis navier stokes system nt u n n n c c ct u c c nf c ut u u u p n u 0 0 1 is considered under boundary conditions of homogeneous neumann type for n and c and dirichlet type for u in a bounded convex domain r with smooth boundary where w and and f are sufficiently smooth given functions generalizing the prototypes const and f s s for s 0 it is known that for all suitably regular initial data n0 c0 and u0 satisfying 0 6 n0 0 c0 0 and u0 0 a corresponding initial boundary value problem admits at least one global weak solution which can be obtained as the pointwise limit of a sequence of solutions to appropriately regularized problems the present paper shows that after some relaxation time this solution enjoys further regularity properties and thereby complies with the concept of eventual energy solutions which is newly introduced here and which inter alia requires that two quasi dissipative inequalities are ultimately satisfied moreover it is shown that actually for any such eventual energy solution n c u there exists a waiting time t0 0 with the property that n c u is smooth in t0 and that n x t n0 c x t 0 and u x t 0 hold as t uniformly with respect to x this resembles a classical result on the three dimensional navier stokes system asserting eventual smoothness of arbitrary weak solutions thereof which additionally fulfill the associated natural energy inequality in consequence our results inter alia indicate that under the considered boundary conditions the possibly destabilizing action of chemotactic cross diffusion in does not substantially affect the regularity properties of the fluid flow at least on large time scales

global existence and boundedness in a keller segel stokes system involving a tensor valued sensitivity with saturation the 3d case abstract in this paper we continue to deal with the initial boundary value problem for the coupled keller segel stokes system n t u n n n s x n c c x t 0 t c t u c c c n x t 0 t u t p u n x t 0 t u 0 x t 0 t where r d is a bounded domain with smooth boundary and the chemotactic sensitivity s is not a scalar function but rather attains values in r d d and satisfies s x n c c s 1 n with some c s 0 and 0 when d 2 our previous work j differential equations 2015 has established the existence of global bounded classical solutions under the subcritical assumption 0 which is consistent with the corresponding results of the fluid free system but the method seems to be invalid in the three dimensional setting in this paper for the case d 3 we develop a new method to establish the existence and boundedness of global classical solutions for arbitrarily large initial data under the assumption 1 2 which is slightly stronger than the corresponding subcritical assumption 1 3 on the fluid free system where such an assumption is essentially necessary and sufficient for the existence of global bounded solutions the key idea here is to establish the general l p regularity of u from a rather low l p regularity of n which will be obtained by a new combinational functional

global existence and large time behavior for a two dimensional chemotaxis navier stokes system abstract this paper concerns the coupled chemotaxis navier stokes system in the two dimensional setting such a system was proposed in 19 to describe the collective effects arising in bacterial suspensions in fluid drops under some basic assumptions on the parameter functions k and the potential function which are consistent with those used by the experimentalists but weaker than those appeared in the known mathematical works we establish the global existence of weak solutions and classical solutions for both the cauchy problem and the initial boundary value problem supplemented with some initial data for the initial boundary value problem we also assert that the solution converges in large time to the spatially homogeneous equilibrium n 0 0 0 with n 0 1 n 0 x d x our results also show that the large diffusion of the cell density or the chemical concentration can rule out the finite time blow up even though the navier stokes fluid is included

boundedness of weak solutions of a chemotaxis stokes system with slow p laplacian diffusion abstract in this paper a chemotaxis stokes system with slow p laplacian diffusion n t u n n p 2 n n c x t 0 c t u c c n c x t 0 u t u p n x t 0 u 0 x t 0 is considered under homogeneous boundary conditions of neumann type for n and c and of dirichlet type for u where is a smooth bounded domain in r 3 and w 2 is a given function it is proved that global bounded weak solutions exist whenever p 23 11

global uniqueness in the inverse scattering problem for the schrodinger operator with external yang mills potentials we consider the schrodinger equation in r n n 3 with external yang mills potentials having compact supports we prove the uniqueness modulo a gauge transformation of the solution of the inverse boundary value problem in a bounded convex domain a similar uniqueness result holds for the inverse scattering problem at a fixed energy

a 3d self consistent chemotaxis fluid system with nonlinear diffusion abstract in this paper we deal with the initial boundary value problem for a chemotaxis fluid model involving a complicated nonlinear coupling term precisely the following self consistent system with porous medium diffusion n t u n n m n c n x t 0 c t u c c n c x t 0 u t p u n n c x t 0 u 0 x t 0 under no flux boundary conditions in a bounded domain r 3 with smooth boundary one of the novelties here is that both the effect of gravity potential force on cells and the effect of the chemotactic force on fluid is considered which leads to the stronger coupling than the most studied chemotaxis fluid model for swimming bacteria proposed in 28 we shall establish the existence of global weak solutions whenever m 4 3 thereby supplementing previously gained knowledge on its two dimensional version

global existence and asymptotic behavior in a two species chemotaxis system with logistic source abstract in this work we consider the two species chemotaxis system with logistic source we present the global existence of generalized solutions under appropriate regularity assumptions on the initial data in addition the asymptotic behavior of the solutions is studied and our results generalize and improve some well known results in the literature

the small convection limit in a two dimensional chemotaxis navier stokes system this paper deals with an initial boundary value problem for the chemotaxis navier stokes system begin aligned left begin array lcll n t u cdot nabla n delta n nabla cdot n nabla c qquad quad x in omega t 0 c t u cdot nabla c delta c nc qquad quad x in omega t 0 u t kappa u cdot nabla u delta u nabla p n nabla phi qquad quad x in omega t 0 nabla cdot u 0 qquad quad x in omega t 0 end array right end aligned in a bounded convex domain omega subset mathbb r 2 with smooth boundary with kappa in mathbb r and a given smooth potential phi omega rightarrow mathbb r it is known that for each kappa in mathbb r and all sufficiently smooth initial data this problem possesses a unique global classical solution n kappa c kappa u kappa the present work asserts that these solutions stabilize to n 0 c 0 u 0 uniformly with respect to the time variable more precisely it is shown that there exist mu 0 and c 0 such that whenever kappa in 1 1 begin aligned big vert n kappa cdot t n 0 cdot t big vert l infty omega big vert c kappa cdot t c 0 cdot t big vert l infty omega quad big vert u kappa cdot t u 0 cdot t big vert l infty omega le c kappa e mu t end aligned for all t 0 this result thereby provides an example for a rigorous quantification of stability properties in the stokes limit process as frequently considered in the literature on chemotaxis fluid systems in application contexts involving low reynolds numbers

a uniqueness theorem for an inverse boundary value problem in electrical prospection we show that a near constant conductivity of a two dimensional body can be uniquely determined by steady state direct current measurements at the boundary mathematically we show that the coefficient in the operator is uniquely determined by its dirichlet integrals

homogenization of dirichlet parabolic problems for coefficients and open sets simultaneously variable and applications to optimal design in a previous paper we studied the homogenization of a sequence of parabolic linear dirichlet problems when the coefficients and the domains vary arbitrarily here we improve the convergence result given in this paper by showing the strong convergence in l2 every time this is applied to obtain an existence result for control problems in optimal design written in a relaxed form the control variables are the material and the shape

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

solutions for semilinear parabolic equations in lp and regularity of weak solutions of the navier stokes system abstract we construct a unique local regular solution in l q 0 t l p for a class of semilinear parabolic equations which includes the semilinear heat equation u t u u u 0 and the navier stokes system here p and q are so chosen that the norm of l q 0 t l p is dimensionless or scaling invariant the main relation between p and q for the semilinear heat equation is 1 q 1 p 1 q n 2 provided that initial data are in l r with r n 2 1 where n is the space dimension applying our regular solutions to the navier stokes system we show that the k 2 dimensional hausdorff measure of possible time singularities of a turbulent solution is zero if the turbulent solution is in l q 0 t l p where k 2 q nq p p n 1 q we show moreover that a turbulent solution is regular if it is in c 0 t l n

global existence and asymptotic stability of the fractional chemotaxis fluid system in r3 abstract in this paper we consider a model arising from biology consisting of fractional chemotaxis equations coupled to viscous incompressible fluid equations throughout transport and external force in r 3 we establish the existence and uniqueness of global solution with small initial data by combining the local existence and a priori estimates as well as continuation argument moreover the decay rates of the solutions and their higher order spatial derivatives are established towards the equilibrium by introducing the negative sobolev space h s 0 s 3 2

global solutions to a 3d chemotaxis stokes system with nonlinear cell diffusion and robin signal boundary condition abstract in this paper we investigate a 3d chemotaxis stokes system with general sensitivity nonlinear cell diffusion and robin signal boundary condition after introducing a lions magenes type transformation we transform the robin signal boundary condition into the usual homogeneous neumann boundary value and then use a two step iterative method to establish the global existence of bounded weak solutions here the key is to deal with the extra terms coming from the transformation in the case of homogeneous robin boundary value we will adapt the method of winkler calc var 2015 35 to investigate the large time behavior and the eventual smoothness of the above weak solutions

asymptotic behaviour of linear dirichlet parabolic problems with variable operators depending on time in varying domains abstract we study the asymptotic behaviour of the solutions of linear parabolic dirichlet problems when the coefficients and the domains where the problems are posed vary simultaneously in the limit problem it appear the h limit of the operators and as it is usual in the homogenization of dirichlet problems a new term of order zero we also obtain a corrector result

an optimal result for global existence and boundedness in a three dimensional keller segel stokes system with nonlinear diffusion abstract this paper investigates the following keller segel stokes system with nonlinear diffusion k s f n t u n n m n c x t 0 c t u c c c n x t 0 u t p u n x t 0 u 0 x t 0 under homogeneous boundary conditions of neumann type for n and c and of dirichlet type for u in a three dimensional bounded domains r 3 with smooth boundary where w 2 m 0 it is proved that if m 4 3 then for any sufficiently regular nonnegative initial data there exists at least one global boundedness solution for system k s f which in view of the known results for the fluid free system mentioned below see introduction is an optimal restriction on m

global solutions for chemotaxis navier stokes system with robin boundary conditions abstract we consider a chemotaxis navier stokes system modelling cellular swimming in fluid drops where an exchange of oxygen between the drop and its environment is taken into account this phenomenon results in an inhomogeneous robin type boundary condition moreover the system is studied without the logistic growth of the bacteria population we prove that in one or two dimensions the system has a unique global classical solution while the existence of a global weak solution is shown in three dimensions in the latter case we show that the energy is bounded uniformly in time a key idea is to introduce and utilise a boundary energy to derive suitable a priori estimates moreover we are able to remove the convexity assumption on the domain

global existence and convergence rates to a chemotaxis fluids system with mixed boundary conditions abstract in this paper we investigate the large time behavior of strong solutions to a chemotaxis fluids system in an unbounded domain with mixed boundary conditions based on the anisotropic l p technique the elliptic estimates and stokes estimates we first establish the global existence of strong solution around the equilibrium state 0 c satn 0 with the help of the continuity arguments where c satn is the saturation value of oxygen inside the fluid then we use de giorgi s technique and energy method to show that such a solution will converge to 0 c satn 0 with an explicit convergence rate in the chemotaxis free case our assumptions and results are consistent with the experimental descriptions and the numerical analysis the novelty here consists of deriving some new elliptic estimates and stokes estimates and choosing a suitable weight in de giorgi s technique to deal with the mixed boundary conditions

identification problems in linear elasticity let be a bounded domain inrnwithc2 boundary and letdbe a lipschitz domain withd we consider the inverse problem determiningd to the system of linear elasticitydi d ij rs ir js d ir js djus 0in where d d rn dand d d rn d under the condition on the lame constants 0 we show thatdis uniquely determined by the complete knowledge of the dirichlet to neumann map we also obtain an uniqueness result for the monotone case from one boundary measurement

abstract lp estimates for the cauchy problem with applications to the navier stokes equations in exterior domains abstract we apply an abstract perturbation theorem to derive global in time lq estimates for the cauchy problem and lq ls estimates for the nonstationary stokes equations in exterior domains this will be applied to obtain various new global in time estimates for weak solutions of the navier stokes equations

asymptotic homogenization in a three dimensional nutrient taxis system involving food supported proliferation abstract the taxis system u t u u v u v u v t d v u v v 1 v is considered in bounded convex domains r n n 1 where d and are positive but and are merely assumed to be nonnegative this particularly includes the special case 0 of a nutrient taxis system with food dependent cell proliferation but beyond that the system for general parameter choices is also used as a model for lotka volterra type interaction involving prey taxis it is firstly shown that if n 5 then for all suitably regular initial data an associated no flux initial boundary value problem admits a global weak solution to the best of our knowledge this inter alia provides the first result on global existence in a system of the form in a spatially three dimensional setting when arbitrarily large initial data and parameters are involved secondly under the additional hypotheses that n 3 0 and 16 d 2 it is seen that each of these solutions becomes eventually smooth and stabilizes toward a spatially homogeneous equilibrium in the sense that 0 1 u t u in l and v t 0 in l as t where u is a constant satisfying u 1 u 0 this on the one hand shows that in comparison to the well understood simple nutrient taxis system obtained on letting 0 and removing the proliferation term u v in the introduction of the latter does not substantially affect the tendency of the system to support relaxation into spatial homogeneity apart from that 0 1 complements previous findings on convergence to equilibria in prey taxis systems of type which seem to exclusively concentrate on cases in which unlike in 0 1 the constant limit functions are a priori known and in which thereby the corresponding asymptotic analysis is apparently simplified to a considerable extent

homogenization of dirichlet parabolic systems with variable monotone operators in general perforated domains we consider the homogenization of parabolic systems with dirichlet boundary conditions when the operators and the domains in which the problems are posed vary simultaneously we assume the operators do not depend on t then we show that the corrector obtained in a previous paper for the elliptic problem still gives a corrector for the parabolic one from this result we easily obtain the limit problem in the parabolic case

eventual smoothness and stabilization of large data solutions in a three dimensional chemotaxis system with consumption of chemoattractant abstract this paper deals with positive solutions of u t u u v x t 0 v t v u v x t 0 under homogeneous neumann boundary conditions in bounded convex domains r 3 with smooth boundary it is shown that for arbitrarily large initial data this problem admits at least one global weak solution for which there exists t 0 such that u v is bounded and smooth in t moreover it is asserted that such solutions approach spatially constant equilibria in the large time limit

global existence and stabilization in a degenerate chemotaxis stokes system with mildly strong diffusion enhancement abstract a class of chemotaxis stokes systems generalizing the prototype n t u n n m 1 n n c c t u c c n c u t p u n u 0 is considered in bounded convex three dimensional domains where w 2 is given the paper develops an analytical approach which consists in a combination of energy based arguments and maximal sobolev regularity theory and which allows for the construction of global bounded weak solutions to an associated initial boundary value problem under the assumption that 0 1 m 9 8 moreover the obtained solutions are shown to approach the spatially homogeneous steady state 1 n 0 0 0 in the large time limit this extends previous results which either relied on different and apparently less significant energy type structures or on completely alternative approaches and thereby exclusively achieved comparable results under hypotheses stronger than 0 1

boundedness in a 2d chemotaxis stokes system with general sensitivity and nonlinear diffusion abstract this paper deals with the following chemotaxis stokes system n t u n n m n s x n c c x t 0 c t u c c n f c x t 0 u t u p n x t 0 u 0 x t 0 in a bounded domain r 2 with smooth boundary w 1 f and s are given sufficiently smooth functions with values in 0 and r 2 2 respectively here s satisfies s x n c s 0 c n with 0 and some nondecreasing nonnegative function s 0 it is showed that when m 1 and 0 the corresponding system possesses a global bounded weak solution for any sufficiently regular initial data n 0 c 0 u 0 satisfying n 0 0 and c 0 0

existence results for chemotaxis shallow water system with degenerate viscosity coefficients and initial vacuum abstract this paper is concerned with the cauchy problem of the chemotaxis shallow water system with degenerate viscosity coefficients a local existence of the unique regular solution is established when the initial data are arbitrarily large and include vacuum moreover a beal kate majda type blow up criterion is provided

eventual smoothness of generalized solutions to a singular chemotaxis stokes system in 2d abstract we study the chemotaxis fluid system n t u n n n c c x t 0 c t u c c n c x t 0 u t p u n x t 0 u 0 x t 0 under homogeneous neumann boundary conditions for n and c and homogeneous dirichlet boundary conditions for u where r 2 is a bounded domain with smooth boundary and c 2 from recent results it is known that for suitable regular initial data the corresponding initial boundary value problem possesses a global generalized solution we will show that for small initial mass n 0 these generalized solutions will eventually become classical solutions of the system and obey certain asymptotic properties moreover from the analysis of certain energy type inequalities arising during the investigation of the eventual regularity we will also derive a result on global existence of classical solutions under assumption of certain smallness conditions on the size of n 0 in l 1 and in l log l u 0 in l 4 and of c 0 in l 2