singular limit for relaxation and viscosity approximations of extended traffic flow models.
stability of conservation laws for a traffic flow model.
-decay of solutions to dissipative-dispersive perturbations of conservation laws
We study the decay in time of the spatial -norm (1 ≤ p ≤ ∞) of solutions to parabolic conservation laws with dispersive and dissipative terms added uₜ - uₓₓₜ - νuₓₓ + buₓ = f(u)ₓ or uₜ + uₓₓₓ - νuₓₓ + buₓ = f(u)ₓ, and we show that under general assumptions about the nonlinearity, solutions of the nonlinear equations have the same long time behavior as their linearizations at the zero solution.
--Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity
We prove the --time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the --time decay estimates.
time decay estimates for the solution of the linear partial differential equations of thermodiffusion
We consider the initial-value problem for a linear hyperbolic parabolic system of three coupled partial differential equations of second order describing the process of thermodiffusion in a solid body (in one-dimensional space). We prove time decay estimates for the solution of the associated linear Cauchy problem.
-resolvent estimates and time decay for generalized thermoelastic plate equations.
estimates for damped wave equations with odd initial data.
L2 Decay for the Navier-Stokes Flow in Halfspaces.
La condition nulle pour les équations hyperboliques en dimension deux d’espace
Laplace asymptotics for generalized K.P.P. equation
Consider a one dimensional nonlinear reaction-diffusion equation (KPP equation) with non-homogeneous second order term, discontinuous initial condition and small parameter. For points ahead of the Freidlin-KPP front, the solution tends to 0 and we obtain sharp asymptotics (i.e. non logarithmic). Our study follows the work of Ben Arous and Rouault who solved this problem in the homogeneous case. Our proof is probabilistic, and is based on the Feynman-Kac formula and the large deviation principle...
Laplace asymptotics for generalized K.P.P. equation
Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation.
Large solutions for the laplacian with a power nonlinearity given by a variable exponent
Large solutions, metasolutions, and asymptotic behaviour of the regular positive solutions of sublinear parabolic problems.
Large solutions of quasilinear elliptic system of competitive type: existence and asymptotic behavior.
Large time behavior for nonlinear higher order convection–diffusion equations
Large time behavior for solutions of nonlinear parabolic problems with sign-changing measure data.
Large time behavior in a density-dependent population dynamics problem with age structure and child care
Two asexual density-dependent population dynamics models with age-dependence and child care are presented. One of them includes the random diffusion while in the other the population is assumed to be non-dispersing. The population consists of the young (under maternal care), juvenile, and adult classes. Death moduli of the juvenile and adult classes in both models are decomposed into the sum of two terms. The first presents death rate by the natural causes while the other describes the environmental...
Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system
This paper deals with a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system. Boundedness, stabilization and blow-up in this system of the fully parabolic and parabolic-elliptic-elliptic versions have already been proved. The purpose of this paper is to derive boundedness and stabilization in the parabolic-parabolic-elliptic version.
Large time behavior of a Cahn-Hilliard-Boussinesq system on a bounded domain.