
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 manydimensional case, we prove the existence of a solution of a general boundaryvalue 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 boundaryvalue 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 Received: 05.07.2007
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., 7:12 (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 12
\pages 316
\mathnet{http://mi.mathnet.ru/dvmg52}
\elib{http://elibrary.ru/item.asp?id=15484736}
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