Semidiscretization for a nonlocal parabolic problem

On the Numerical Solution of the Diffusion Equation with a Nonlocal Boundary Condition

Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The method of lines (M...

Convergent Semidiscretization of a Nonlinear Fourth Order Parabolic System

Existence and uniqueness of solutions for a nonlocal parabolic thermistor-type problem

In this paper we prove existence and uniqueness of solutions to the nonlocal parabolic problem ∂u ∂t −△pu = λ f(u)

Nonlocal Boundary Value Problems for Elliptic-Parabolic Differential and Difference Equations

The abstract nonlocal boundary value problem −d2u t /dt2 Au t g t , 0 < t < 1, du t /dt − Au t f t , 1 < t < 0, u 1 u −1 μ for differential equations in a Hilbert space H with the self-adjoint positive definite operator A is considered. The well-posedness of this problem in Hölder spaces with a weight is established. The coercivity inequalities for the solution of boundary value problems for el...

On Finite-time Blow-up for a Nonlocal Quasi-linear Parabolic Problem Describing Shear Bands in Metals

In this paper we investigate results on finite-time blow-up of solutions to a nonlocal quasi-linear parabolic problem. We extend some known results to higher dimensions. AMS subject classification: 35K55, 35K65, 35B35.