Time analyticity for solutions of nonlinear abstract parabolic evolution equations
We study analyticity with respect to time of the solutions to a class of nonlinear evolution equations in Banach space. The results are applied to Cauchy-Dirichlet problems for fully nonlinear parabolic integrodifferential equations such as \[ u_ t(t,x)=f(t,x,u(t,x),\nabla u(t,x),\Delta u(t,x))+\int^{t}_{0}g(t,s,x,u(s,x),\nabla u(s,x),\Delta u(s,x))ds, \] \(t\geq 0\), \(x\in {\bar \Omega}\), where \(\Omega\) is a regular bounded open set in \({\mathbb{R}}^ n\).
scientific article; zbMATH DE number 4069417