Verification of asymptotic solutions for one-dimensional nonlinear parabolic equations

S. A. Vakulenko

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

Abstract: The present article proves a result that is new for partial differential equations. According to this result, the solution of the Cauchy problem for a nonlinear parabolic equation with variable, slowly changing coefficients will turn into (asymptotically approach) a special asymptotic solution, either a solution or a kink, for high values of $t$.

UDC: 517

Received: 20.04.1992

 English version: Mathematical Notes, 1992, 52:3, 875–880

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