Existence and regularity of a global attractor for doubly nonlinear parabolic equations.
Existence and stability of periodic solutions for a nonlocal evolution population problem.
The theory of maximal monotone operators is applied to prove the existence of weak periodic solutions for a nonlinear nonlocal problem. The stability of these solutions is a consequence of the Lipschitz continuous assumption on the diffusivity matrix and the death rate.
Existence and stability theorems for abstract parabolic equations, and some of their applications
For a class of semi-abstract evolution equations for sections on vector bundles on a three-dimensional compact manifold we prove that for initial values with certain symmetries strong solutions exist for all times. In case these solutions become small after some time, strong solutions exist also for small perturbations of these initial values. Many systems from fluid mechanics are included in this class.
Existence and uniqueness for the nonstationary problem of the electrical heating of a conductor due to the Joule-Thomson effect.
Existence and uniqueness for the three-dimensional thermoelasticity system in shape memory problems
A thermodynamically consistent model of shape memory alloys in three dimensions is studied. The thermoelasticity system, based on the strain tensor, its gradient and the absolute temperature, generalizes the well-known one-dimensional Falk model. Under simplifying structural assumptions we prove global in time existence and uniqueness of the solution.
Existence and uniqueness of classical solutions to certain nonlinear integro-differential Fokker-Planck type equations.
Existence and uniqueness of periodic solutions for a model of contaminant flow in porous medium.
Existence and uniqueness of solutions for a degenerate quasilinear parabolic problem.
We consider the following quasilinear parabolic equation of degenerate type with convection term ut = φ (u)xx + b(u)x in (-L,0) x (0,T). We solve the associate initial-boundary data problem, with nonlinear flux conditions. This problem describes the evaporation of an incompressible fluid from a homogeneous porous media. The nonlinear condition in x = 0 means that the flow of fluid leaving the porous media depends on variable meteorological conditions and in a nonlinear manner on u. In x = -L we...
Existence and uniqueness of solutions for a three-dimensional thermoelastic system [Book]
Existence and Uniqueness of Solutions of Nonlinear Neumann Problems.
Existence et unicité de la solution pour un système de deux E.D.P.
We give some results on the existence, uniqueness and regularity of a nonlinear evolution system. This system models the viscoelastic behaviour of unicellular marine alga Acetabularia mediterrania when the calcium concentration varies. We show (with the aid of a fixed-point theorem) that the system admits a unique local solution in time.
Existence of a solution for the initial boundary value problem for a high order parabolic equation in an unbounded domain.
Existence of extremal periodic solutions for quasilinear parabolic equations.
Existence of global solution for a nonlocal parabolic problem.
Existence of periodic solutions for semilinear parabolic equations
In this paper, we are concerned with the semilinear parabolic equation ∂u/∂t - Δu = g(t,x,u) if u = 0 if , where is a bounded domain with smooth boundary ∂Ω and is T-periodic with respect to the first variable. The existence and the multiplicity of T-periodic solutions for this problem are shown when g(t,x,ξ)/ξ lies between two higher eigenvalues of - Δ in Ω with the Dirichlet boundary condition as ξ → ±∞.
Existence of stable periodic solutions for quasilinear parabolic problems in the presence of well-ordered lower and upper-solutions.
Existence of stable periodic solutions of a semilinear parabolic problem under Hammerstein-type conditions.
Existence Results for Doubly Nonlinear Higher Order Parabolic Equations on Unbounded Domains.
Explicit exponential decay bounds in quasilinear parabolic problems.
Exponential stability of positive solutions to some nonlinear heat equations.