Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Antontsev S.  

Wave Equation with p(x,t)- Laplacian and Damping Term: Existence and Blow-up

We consider the Dirichlet problem for wave equations with p(x,t)- Laplacian and damping term. Under suitable condition on the data, we prove local and global existence theorems and study the finite time blow-up of the solutions. The analysis relies on the methods developed in :

[1.] Antontsev S.N., Díaz J.I., Shmarev S.I. Energy Methods for Free Boundary Problems: Applications to Non-linear PDEs and Fluid Mechanics. Bikhauser, Boston, 2002. Progress in Nonlinear Differential Equations and Their Applications, Vol. 48.
[2.] Antontsev S.N., Shmarev S. Blow-up of solutions to parabolic equations with nonstandard growth conditions // J. Comput. Appl. Math., 234 (2010), pp.2633--2645.
[3.] Antontsev S.N., Shmarev S. Anisotropic parabolic equations with variable nonlinearity // Publicacions. Sec. Mat. Univ. Autonoma Barcelona, (2009), pp.355--399.

Abstracts file: NIK-90-Antontsev.pdf
Full text file: NIK_NIK_90_Antontsev.pdf

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