This article is cited in 4 papers

Solution blowup for systems of shallow-water equations

M. O. Korpusov, E. V. Yushkov

Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider initial-boundary value problems for systems of shallow-water equations. Using the test-function method proposed by Pokhozhaev and Mitidieri, we study the effects of the boundary values and initial conditions on the occurrence, duration, and rate of blowup of the solutions of these problems. Under natural boundary conditions, we prove the existence of blowup in one- and two-dimensional problems in bounded and unbounded regions with dissipation and dispersion.

Keywords: initial-boundary value problem, finite-time blowup, shallow water approximation.

Received: 02.02.2013

DOI: 10.4213/tmf8509

 English version: Theoretical and Mathematical Physics, 2013, 177:2, 1505–1514

Bibliographic databases:

• 
• 
• 
• 
• 
• 
•