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 periodic solutions for a nonlinear reaction-diffusion problem.
We consider a class of degenerate reaction-diffusion equations on a bounded domain with nonlinear flux on the boundary. These problems arise in the mathematical modelling of flow through porous media. We prove, under appropriate hypothesis, the existence and uniqueness of the nonnegative weak periodic solution. To establish our result, we use the Schauder fixed point theorem and some regularizing arguments.
Existence and uniqueness of solutions Cauchy problem for nonlinear infinite systems of parabolic differential-functional equations.
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 for gradient systems without a compactness embedding condition
This paper is devoted to the existence and uniqueness of solutions for gradient systems of evolution which involve gradients taken with respect to time-variable inner products. The Gelfand triple considered in the setting of this paper is such that the embedding is only continuous.
Existence and uniqueness of solutions of nonlinear infinite systems of parabolic differential-functional equations
We consider the Fourier first initial-boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations of parabolic type. The right-hand sides of the system are functionals of unknown functions. The existence and uniqueness of the solution are proved by the Banach fixed point theorem.
Existence and Uniqueness of Solutions of Nonlinear Neumann Problems.
Existence and uniqueness of solutions of system governed by second order quasilinear integro-partial differential equation of parabolic type.
Existence and uniqueness of very singular solution of a degenerate parabolic equation with nonlinear convection.
Existence and uniqueness result for a class of nonlinear parabolic equations with L¹ data
We prove the existence and uniqueness of a renormalized solution for a class of nonlinear parabolic equations with no growth assumption on the nonlinearities.
Existence and uniqueness to the Cauchy problem for linear and semilinear parabolic equations with local conditions⋆
We consider the Cauchy problem in ℝd for a class of semilinear parabolic partial differential equations that arises in some stochastic control problems. We assume that the coefficients are unbounded and locally Lipschitz, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution by approximation with linear parabolic equations. The linear equations involved can not be solved with the traditional...
Existence and upper semicontinuity of uniform attractors in for nonautonomous nonclassical diffusion equations
We prove the existence of uniform attractors in the space for the nonautonomous nonclassical diffusion equation , ε ∈ [0,1]. The upper semicontinuity of the uniform attractors at ε = 0 is also studied.
Existence, comportement à l'infini et stabilité dans certains problèmes quasilinéaires elliptiques et paraboliques d'ordre 2
Existence de la trace initiale pour des solutions d'une équation parabolique dégénérée
Existence de la trace initiale pour des solutions d'une équation parabolique dégénérée
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.