Reconstruction of source function for parabolic equations with variable exponents

2015

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DOI 10.1063/1.4930466
Data confidence 70 medium
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Abstract

We study the inverse problem of reconstructing the right side for nonlinear parabolic equation with integral overdetermination. We prove the unique solvability of this problem. By using the method of successive approximations, the existence and uniqueness theorem for the solution of the inverse problem is proved. The proof of the uniqueness of a generalized solution is based on obtained a priori estimate.