This article is cited in 7 papers

Local solvability and blowup of the solution of the Rosenau–Bürgers equation with different boundary conditions

A. A. Panin

Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider several models of initial boundary-value problems for the Rosenau–Bürgers equation with different boundary conditions. For each of the problems, we prove the unique local solvability in the classical sense, obtain a sufficient condition for the blowup regime, and estimate the time of the solution decay. The proof is based on the well-known test-function method.

Keywords: blowup regime, local solvability, noncontinuable solution, Rosenau–Bürgers equation.

Received: 29.01.2013

DOI: 10.4213/tmf8507

 English version: Theoretical and Mathematical Physics, 2013, 177:1, 1361–1376

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