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On three-point boundary value problem with a weighted integral condition for a class of singular parabolic equations. (English) Zbl 1014.35039

Summary: We deal with a three-point boundary value problem for a class of singular parabolic equations with a weighted integral condition in place of one of standard boundary conditions. We will first establish an a priori estimate in weighted spaces. Then, we prove the existence, uniqueness, and continuous dependence of a strong solution.

MSC:

35K20 Initial-boundary value problems for second-order parabolic equations
35B45 A priori estimates in context of PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
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