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A boundary value problem with multivariables integral type condition for parabolic equations. (English) Zbl 1197.35131
Summary: We study a boundary value problem with multivariables integral type condition for a class of parabolic equations. We prove the existence, uniqueness, and continuous dependence of the solution upon the data in the functional weighted Sobolev spaces. Results are obtained by using a functional analysis method based on two-sided a priori estimates and on the density of the range of the linear operator generated by the considered problem.

35K20 Initial-boundary value problems for second-order parabolic equations
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