Stability of solutions of evolution equations

Abstract

While the choice of a norm in the space where an evolution problem is posed is ineffective as far as the smoothness properties of the solution with respect to the space variables are concerned, the asymptotic behavior of this solution when $t\to +\infty$ is greatly effected by a change of the norm in the space. We illustrate this consideration by studying existence, uniqueness and asymptotic behavior for the solution of a simple but very significant evolution problem.