This article is cited in 6 papers

Differentical equations, dynamical systems and optimal control

Initial boundary value problem for a nonlocal in time parabolic equation

V. N. Starovoitov

Lavrentyev Institute of Hydrodynamics, pr. Lavrentyeva, 15, 630090, Novosibirsk, Russia

Abstract: This paper deals with a quasi-linear parabolic partial differential equation that includes a nonlocal in time term. This term contains the integral of the solution over the entire time interval, where the problem is considered. The weak solvability of the initial boundary value problem for this equation is proven.

Keywords: nonlocal in time parabolic equation, initial boundary value problem, solvability.

UDC: 517.956.4

MSC: 35K58

Received August 31, 2018, published October 30, 2018

Language: English

DOI: 10.17377/semi.2018.15.107

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