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.

UDC: 517.95

MSC: 35M10

Received: 05.07.2007

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