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 Dal'nevost. Mat. Zh., 2007, Volume 7, Number 1-2, Pages 3–16 (Mi dvmg52)

Solvability of nonlinear heat equation in class of unbounded functions with degeneration of coefficient near derivative with respect to time

E. G. Agapova

Pacific National University

Abstract: In this paper, we consider quasilinear parabolic equations which degenerate on a solution due to a multiplier of the derivative with respect to time. In the many-dimensional case, we prove the existence of a solution of a general boundary-value problem from a class of unbounded functions. Restrictions to nonlinearity of the multiplier of the derivative with respect to time are different from ones considered before by other authors.

Key words: nonlinear heat equation, quasilinear parabolic equations, unbounded functions, degenerate on a solution, a general boundary-value problem, class of unbounded functions, nonlinearity of the multiplier of the derivative with respect to time.

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UDC: 517.95
MSC: 35M10

Citation: E. G. Agapova, “Solvability of nonlinear heat equation in class of unbounded functions with degeneration of coefficient near derivative with respect to time”, Dal'nevost. Mat. Zh., 7:1-2 (2007), 3–16

Citation in format AMSBIB
\Bibitem{Aga07} \by E.~G.~Agapova \paper Solvability of nonlinear heat equation in class of unbounded functions with degeneration of coefficient near derivative with respect to time \jour Dal'nevost. Mat. Zh. \yr 2007 \vol 7 \issue 1-2 \pages 3--16 \mathnet{http://mi.mathnet.ru/dvmg52} \elib{https://elibrary.ru/item.asp?id=15484736}