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A three-point boundary value problem with an integral two-space-variables condition for parabolic equations. (English) Zbl 1124.35319

Summary: We study a three-point boundary value problem with an integral two-space-variables condition for a class of parabolic equations. The existence and uniqueness of the solution in the functional weighted Sobolev space are proved. The proof is based on two-sided a priori estimates and on the density of the range of the operator generated by the problem considered.

MSC:

35K20 Initial-boundary value problems for second-order parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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