Ukrainian Mathematical Bulletin

Volume 1, Issue 2, 2004 pp. 265-278.

Phase Spaces for a Class of Sobolev-Type Equations

Authors: Georgy A. Sviridyuk
Author institution: Chelyabinsk State University, Chelyabinsk, Russia

Summary: The solvability of the Cauchy problem $u(0)=u_0$ for a semilinear differential operator equation $L\dot u = Mu + N(u)$ is considered. 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.

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