This article is cited in 5 papers

On exact solutions of a nonclassical partial differential equation

A. I. Aristov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

Abstract: For a nonclassical nonlinear partial differential equation, several classes of solutions expressed in terms of elementary and special functions are constructed. Moreover, solutions of one of the classes contain an arbitrary sufficiently smooth function of a single argument. It is shown that, among these solutions, there are ones going to infinity in a finite time (blowing up) and ones that are bounded on any finite time interval.

Key words: nonlinear partial differential equations, exact solutions, solution blowup.

UDC: 519.63

MSC: Primary 35G20; Secondary 35B44, 35C05

Received: 26.01.2015

DOI: 10.7868/S0044466915110046

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:11, 1836–1841

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