Nonlinear analytic semiflows

Source abstract

Synopsis In this paper a local existence and regularity theory is given for nonlinear parabolic initial value problems ( x ′( t ) = f ( x ( t ))), and quasilinear initial value problems ( x ′( t )= A ( x ( t )) x ( t ) + f ( x ( t ))). This theory extends the theory of DaPrato and Grisvard of 1979, and shows how various properties, like analyticity of solutions, can be derived as a direct corollary of the existence theorem.