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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2004 Volume 76, Issue 6, Pages 840–853 (Mi mzm156)

This article is cited in 64 papers

A Nonlinear Loaded Parabolic Equation and a Related Inverse Problem

A. I. Kozhanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

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 $\bar u(x,t)= \alpha(t)u(x,t)+\int^t_0\beta(\tau)u(x,\tau)\,d\tau$ 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.

UDC: 517.946

Received: 26.12.2001

DOI: 10.4213/mzm156


 English version:
Mathematical Notes, 2004, 76:6, 784–795

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