This article is cited in 10 papers

On the Initial Boundary-Value Problem for a Nonlinear Sobolev-Type Equation with Variable Coefficient

A. I. Aristov


Abstract: We study the initial boundary-value problem for a nonlinear Sobolev-type equation with variable coefficient. We obtain sufficient conditions for both global and local (in time) solvability. In the case of local (but not global) solvability, we obtain upper and lower bounds for the existence time of the solution in the form of explicit and quadrature formulas.

Keywords: nonlinear Sobolev-type equation, initial boundary-value problem, existence time of a solution, Boussinesq equation, Hölder's inequality, blow-up of a solution.

UDC: 517.955.8

Received: 29.12.2010
Revised: 29.09.2011

DOI: 10.4213/mzm9018

 English version: Mathematical Notes, 2012, 91:5, 603–612

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