Obstacle identification problems for parabolic equations and systems are considered. Unique continuation property plays an important role in the arguments. These arguments are based on the idea which was first used in the paper MR0847528 (87k:35248) of one of the authors earlier. The technique is applied to inverse problems for slightly compressible fluids and to inverse problems for the heat e...

We study the solutions of a parabolic system of heat equations coupled at the boundary through a nonlinear flux. We characterize in terms of the parameters involved when nonsimultaneous quenching may appear. Moreover, if quenching is non-simultaneous we find the quenching rate, which surprisingly depends on the flux associated to the other component.

Parabolic equations with unbounded coefficients and even generalized functions (in particular Dirac–delta functions) model large–scale of problems in the heat–mass transfer. This paper provides estimates for the convergence rate of difference scheme in discrete Sobolev like norms, compatible with the smoothness of the differential problems solutions, i.e with the smoothness of the input data.

The minimal positive solutions of the heat equation on A' X (-00, 7") are determined for X a homogeneous Riemannian space. A simple proof of uniqueness for the positive Cauchy problem on a homogeneous space is given using Choquet's theorem and the explicit form of these solutions. Introduction. A minimal solution of a linear elliptic or parabolic equation is a nonnegative solution u such that, ...

We discuss the use of the WKB ansatz in a variety of parabolic problems involving a small parameter. We analyse the Stefan problem for small latent heat, the Black–Scholes problem for an American put option, and some nonlinear diffusion equations, in each case constructing an asymptotic solution by the use of ray methods.

This paper is concerned with linear uniformly elliptic and parabolic partial differential equations in divergence form. It is assumed that the coefficients of the equations are random variables, constant in time. The Green’s functions for the equations are then random variables. Regularity properties for expectation values of Green’s functions are obtained. In particular, it is shown that the e...

This study investigates mixed convection heat transfer about a thin vertical plate in the presence of magneto and conjugate heat transfer effects in the porous medium with high porosity. The fluid is assumed to be incompressible and dense. The nonlinear coupled parabolic partial differential equations governing the flow are transformed into the nonsimilar boundary layer equations, which are the...

This chapter presents some applications of nonstandard finite difference methods to general nonlinear heat transfer problems. Nonlinearity in heat transfer problems arises when i. Some properties in the problem are temperature dependent ii. Boundary conditions are described by nonlinear functions iii. The interface energy equation in phase change problems is nonlinear. Free convection and surfa...

we focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of it¨o type, in particular, parabolic equations. the main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

In this paper we will prove a maximum principle for the solutions of linear parabolic equation on complete non-compact manifolds with a time varying metric. We will prove the convergence of the Neumann Green function of the conjugate heat equation for the Ricci flow in Bk × (0, T ) to the minimal fundamental solution of the conjugate heat equation as k → ∞. We will prove the uniqueness of the f...