Pseudodifferential parabolic equations in uniform spaces

Abstract

The paper is devoted to local and global solvability in locally uniform spaces and to the existence of a global attractor for a parabolic problem containing fractional power of the minus Laplace operator. Several useful technical tools and estimates are also collected in this paper.

Keywords:

• fractal parabolic equation
• fractional powers of sectorial operator
• locally uniform spaces
• global solution
• global attractor

AMS Subject Classifications:

• 35S10
• 35B40
• 35K90

Acknowledgments

The authors are very grateful to the anonymous referees for their comments improving the original version of the paper. T. Dlotko and M.B. Kania were supported by NCN grant DEC-2012/05/B/ST1/00546 (Poland), C.Sun was supported by NSFC Grants 11031003, 11171028, 11271174 and