Stability of stationary solutions for semilinear heat equations with concave nonlinearity
Stability of stationary solutions for semilinear heat equations with concave nonlinearity
This paper is concerned with the stability analysis of stationary solutions of the Cauchy–Dirichlet problem for some semilinear heat equation with concave nonlinearity. The instability of sign-changing solutions is verified under some variational assumption. Moreover, the exponential stability of the positive stationary solution at an optimal rate is proved by …