On linear higher-order parabolic equations in Morrey spaces

Abstract

In this paper, linear higher-order parabolic equation is shown to define a semigroup in Morrey spaces. For higher-order diffusion equation, the associated semigroup is proved analytic and sharp semigroup estimates in Morrey scale are derived. The analysis also includes semigroups in Morrey scale related to solving linear higher-order fractional diffusion equations.