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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 718–731 (Mi semr1090)  

Differentical equations, dynamical systems and optimal control

Degenerating parabolic equations with a variable direction of evolution

A. I. Kozhanova, E. E. Macievskayab

a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 2, Pirogova str., Novosibirsk, 630090, Russia

Abstract: The aim of the paper is to study the solvability in the classes of regular solutions of boundary value problems for differential equations
$$ \varphi(t)u_t-\psi(t)\Delta u+c(x,t)u=f(x,t)\quad (x\in\Omega\subset \mathbb{R}^n,\quad 0<t<T). $$
A feature of these equations is that the function $\varphi (t)$ in them can arbitrarily change the sign on the segment $[0, T]$, while the function $\psi (t)$ is nonnegative for $t \in [0, T]$. For the problems under consideration, we prove existence and uniqueness theorems.

Keywords: degenerate parabolic equations, variable direction of evolution, boundary value problems, regular solutions, existence, uniqueness.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-51-41009__


DOI: https://doi.org/10.33048/semi.2019.16.048

Full text: PDF file (182 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.946
MSC: 35R30, 35K20, 35L20
Received February 5, 2019, published June 4, 2019

Citation: A. I. Kozhanov, E. E. Macievskaya, “Degenerating parabolic equations with a variable direction of evolution”, Sib. Èlektron. Mat. Izv., 16 (2019), 718–731

Citation in format AMSBIB
\Bibitem{KozMac19}
\by A.~I.~Kozhanov, E.~E.~Macievskaya
\paper Degenerating parabolic equations with a variable direction of evolution
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 718--731
\mathnet{http://mi.mathnet.ru/semr1090}
\crossref{https://doi.org/10.33048/semi.2019.16.048}


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