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Continuous dependence of solutions to mixed boundary value problems for a parabolic equation. (English) Zbl 1136.35312

Summary: We prove the continuous dependence, upon the data, of solutions to second-order parabolic equations. We study two boundary-value problems: One has a nonlocal (integral) condition and the another has a local boundary condition. The proofs are based on a priori estimate for the difference of solutions.

MSC:

35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35B45 A priori estimates in context of PDEs
35K30 Initial value problems for higher-order parabolic equations
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