Phase spaces for a class of Sobolev type equations

Abstract

The solvability of the Cauchy problem u(0) = u₀ of an semilinear differential operator equation Lǔ = Mu+N(u) is under consideration. The abstract results are illustrated by the Cauchy–Dirichlet problem for degenerate reaction-diffusion equations and for Navier–Stokes equations, and by the Cauchy–Bernard problem for Oskolkov thermoconvection equations.