Linearized Stability for Nonlinear Partial Differential Delay Equations

Abstract

AbstractThe object of the paper are partial differential delay equations of the form \( \dot{u}(t)+Bu(t)\ni\,F(u_{t}),\,t \geq 0,\,u_{0} = \varphi \), with \( B\,\subset\,X\,\times\,X\,\omega \)-accretive in a Banach space X. We extend the principle of linearized stability around an equilibrium from the semilinear case, with B linear, to the fully nonlinear case, with B having a linear ‘resolvent-differential’ at the equilibrium.KeywordsNonlinear partial differential delay equationsaccretive operatorslinearized stabilitysubtangential conditions.