A problem with nonlocal conditions for a one-dimensional parabolic equation

A. B. Beylin ; A. V. Bogatov ; L. S. Pulkina

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 2, pp. 380-395.

Résumé

In present paper, we consider a problem with nonlocal conditions for parabolic equation and show that there exists a unique weak solution in Sobolev space. The main tool to prove the existence of a unique weak solution to the problem is a priori estimates derived by authors. We also note a connection between Steklov nonlocal conditions and first kind integral conditions. This connection enables interpret the problem under consideration as a problem with perturbed Steklov nonlocal conditions. Obtained results may be useful for certain class of problems including inverse problems.

Détail

Mots-clés : parabolic equation, nonlocal conditions
Keywords: boundary-value problem, generalized solution; Sobolev spaces.

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