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A Nonlinear Loaded Parabolic Equation and a Related Inverse Problem

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Abstract

The solvability of the nonlocal-in-time boundary-value problem for the nonlinear parabolic equation

$$u_t - \Delta u + c(\bar u(x,T))u = f(x,t),$$

where \(\bar u(x,t) = \alpha (t)u(x,t) + \int_0^t {\beta (\tau )u(x,\tau )d\tau } \) for given functions \(\alpha (t)\) and \(\beta (t)\), is studied. Existence and uniqueness theorems for regular solutions are proved; it is shown that the results obtained can be used to study the solvability of coefficient inverse problems.

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Authors and Affiliations

  1. S. L. Sobolev Institute of Mathematics, Siberian Division, Russian Academy of Sciences, Russia

    A. I. Kozhanov

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  1. A. I. Kozhanov
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Kozhanov, A.I. A Nonlinear Loaded Parabolic Equation and a Related Inverse Problem. Mathematical Notes 76, 784–795 (2004). https://doi.org/10.1023/B:MATN.0000049678.16540.a5

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  • DOI: https://doi.org/10.1023/B:MATN.0000049678.16540.a5

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