Three-level difference schemes on non-uniform in time grids.
Time analyticity and backward uniqueness for the Boussinesq equations
We prove that strong solutions of the Boussinesq equations in 2D and 3D can be extended as analytic functions of complex time. As a consequence we obtain the backward uniqueness of solutions.
Time and space Sobolev regularity of solutions to homogeneous parabolic equations
We give necessary and sufficient conditions on the initial data such that the solutions of parabolic equations have a prescribed Sobolev regularity in time and space.
Time asymptotic description of an abstract Cauchy problem solution and application to transport equation
In this paper, we study the time asymptotic behavior of the solution to an abstract Cauchy problem on Banach spaces without restriction on the initial data. The abstract results are then applied to the study of the time asymptotic behavior of solutions of an one-dimensional transport equation with boundary conditions in -space arising in growing cell populations and originally introduced by M. Rotenberg, J. Theoret. Biol. 103 (1983), 181–199.
Time averaging for random nonlinear abstract parabolic equations.
Time averaging for the strongly confined nonlinear Schrödinger equation
Time Decay for Nonlinear Wave Equations in Two Space Dimensions.
Time Decay for Some Schrödinger Equations.
Time decay of finite energy solutions of the non linear Klein-Gordon and Schrödinger equations
Time decay of solutions to the Schrödinger equation in exterior domains. II
Time decay of solutions to the Schrödinger equation in exterior domains. I
Time estimates for the Cauchy problem for a third-order hyperbolic equation.
Time periodic solutions to a nonhomogeneous Dirichlet periodic problem.
Time-decay of scattering solutions and classical trajectories
Time-dependent invariant regions for parabolic systems related to one- dimensional nonlinear elasticity
A parabolic system arisng as a viscosity regularization of the quasilinear one-dimensional telegraph equation is considered. The existence of - a priori estimates, independent of viscosity, is shown. The results are achieved by means of generalized invariant regions.
Time-evolution of a caustic.
Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods
The author investigates time-periodic solutions of the quasilinear beam equation with the help of accelerated convergence methods. Using the Newton iteration scheme, the problem is approximated by a sequence of linear equations solved via the Galerkin method. The derivatiove loss inherent to this kind of problems is compensated by taking advantage of smoothing operators.
Time-periodic solutions of quasilinear parabolic differential equations II. Oblique derivative boundary conditions
We study boundary value problems for quasilinear parabolic equations when the initial condition is replaced by periodicity in the time variable. Our approach is to relate the theory of such problems to the classical theory for initial-boundary value problems. In the process, we generalize many previously known results.
Time-periodic solutions of telegraph equations in spatial variables
Time-periodic weak solutions.