# Stable equilibria with variable diffusion

Chipot, M; Hale, J (1983). Stable equilibria with variable diffusion. In: Smoller, J A. Nonlinear partial differential equations (Durham, N.H. 1982). Providence, RI: American Mathematical Society , 209-213.

## Abstract

For a scalar nonlinear parabolic equation in one space dimension with homogeneous Neumann boundary conditions, criteria are given on the diffusion coefficient to ensure that the stable equilibrium solutions are constant functions regardless of the nonlinearities. The Dirichlet problem is also discussed.

For a scalar nonlinear parabolic equation in one space dimension with homogeneous Neumann boundary conditions, criteria are given on the diffusion coefficient to ensure that the stable equilibrium solutions are constant functions regardless of the nonlinearities. The Dirichlet problem is also discussed.