Linear parabolic equations with venttsel initial boundary conditions

Necessary Optimality Conditions for Some Control Problems of Elliptic Equations with Venttsel Boundary Conditions

In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a contro...

Initial - Boundary Value Problems for Parabolic Equations

Attractors for Parabolic Equations with Nonlinear Boundary Conditions, Critical Exponents, and Singular Initial Data

Linear Stochastic Differential Equations with Boundary Conditions

We study linear stochastic differential equations with affine boundary conditions. The equation is linear in the sense that both the drift and the diffusion coefficient are affine functions of the solution. The solution is not adapted to the driving Brownian motion, and we use the extended stochastic calculus of Nualar t and Pardoux [16] to analyse them. We give analytical necessary and suffici...

On Comparison Principles for Parabolic Equations with Nonlocal Boundary Conditions

The positivity of solutions for parabolic problems is the base of comparison principle which is important in monotonic methods used for these problems. Recently, Yin [1] developed several results in applications of the comparison principle, especially on nonlocal problems. Earlier works on problems with nonlocal boundary conditions can be found in [2], and some of references can be found in [1,...