We study the well-posedness of triply nonlinear degenerate ellipticparabolic-hyperbolic problem b(u)t − div ã(u, ∇φ(u)) + ψ(u) = f, u|t=0 = u0 in a bounded domain with homogeneous Dirichlet boundary conditions. The nonlinearities b, φ and ψ are supposed to be continuous non-decreasing, and the nonlinearity ã falls within the Leray-Lions framework. Some restrictions are imposed on the dependence...

We prove convergence of the solutions Xn of semilinear stochastic evolution equations on a Banach space B, driven by a cylindrical Brownian motion in a Hilbert space H, dXn(t) = (AnX(t) + Fn(t,Xn(t))) dt+Gn(t,Xn(t)) dWH(t), Xn(0) = ξn, assuming that the operators An converge to A and the locally Lipschitz functions Fn and Gn converge to the locally Lipschitz functions F and G in an appropriate ...

This paper is devoted to the study of the existence, uniqueness, continuous dependence and spatial behaviour of the solutions for the backward in time problem determined by the Type III with two temperatures thermoelastodynamic theory. We first show the existence, uniqueness and continuous dependence of the solutions. Instability of the solutions for the Type II with two temperatures theory is ...

These notes provide an introduction to the theory of hyperbolic systems of conservation laws in one space dimension. The various chapters cover the following topics: 1. Meaning of the conservation equations and definition of weak solutions. 2. Shocks, Rankine-Hugoniot equations and admissibility conditions. 3. Genuinely nonlinear and linearly degenerate characteristic fields. Solution to the Ri...

We prove continuous dependence on the intensity coefficient and continuous dependence on the external data in the theory of magneto-elasticity. We do not require the Lamé coefficients to be positive. We use logarithmic convexity arguments similar to those of Ames and Straughan (1992) in classical thermoelasticity. 1. Introduction. In recent years, much attention has been directed to the knowled...

Global existence, uniqueness and continuous dependence on initial data are established for a quasilinear functional reaction-diiusion equation which arises from a two-dimensional energy balance climate model. Our approach relies heavily on the so-called stability estimates for linear evolution equations of parabolic type (cf. 6]).

In this paper, we prove the existence, uniqueness, and continuous dependence of the mild solutions for a class of fractional abstract differential equations with infinite delay. The results are obtained by using the Krasnoselskii’s fixed point theorem and the theory of resolvent operators for integral equations.

This manuscript is devoted to the study of existence, uniqueness and stability results neutral stochastic differential equations with random impulses. The existence are obtained by considering sufficient conditions applying fixed point theory aforementioned system. proved via continuous dependence on initial value. Finally an example provided show effectiveness result.