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Mat. Zametki, 2012, Volume 92, Issue 4, Pages 567–582 (Mi mz9015)  

Blow-Up of the Solution of the Initial Boundary-Value Problem for the Generalized Boussinesq Equation with Nonlinear Boundary Condition

P. A. Makarov

Tikhomirov Instrument Engineering Research Institute

Abstract: The initial boundary-value problem for a nonlinear equation of pseudoparabolic type with nonlinear Neumann boundary condition is considered. We prove a local theorem on the existence of solutions. Using the method of energy inequalities, we obtain sufficient conditions for the blow-up of solutions in a finite time interval and establish upper and lower bounds for the blow-up time.

Keywords: Boussinesq equation, pseudoparabolic-type equation, initial boundary-value problem, Neumann boundary condition, blow-up of solutions, homogenous isotropic semiconductor, Galerkin's method, dissipative processes in a semiconductor

DOI: https://doi.org/10.4213/mzm9015

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English version:
Mathematical Notes, 2012, 92:4, 519–531

Bibliographic databases:

UDC: 517.958:531.32
Received: 07.10.2010

Citation: P. A. Makarov, “Blow-Up of the Solution of the Initial Boundary-Value Problem for the Generalized Boussinesq Equation with Nonlinear Boundary Condition”, Mat. Zametki, 92:4 (2012), 567–582; Math. Notes, 92:4 (2012), 519–531

Citation in format AMSBIB
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