The initial-boundary value problems for parabolic equations in domains with conical points. (English) Zbl 1328.35072

Summary: We consider a initial-boundary value problem for parabolic equation in a domain with conical points. We establish the weak well-posedness of the problem and the regularity of the solution. We also receive asymptotic formulas for the solution near the conical points.


35K35 Initial-boundary value problems for higher-order parabolic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35B40 Asymptotic behavior of solutions to PDEs
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35B65 Smoothness and regularity of solutions to PDEs