Международная конференция
«Современные проблемы прикладной математики и механики: теория, эксперимент и практика», посвященная 90-летию со дня рождения академика Н.Н. Яненко
№ гос. регистрации 0321101160, ISBN 978-5-905569-01-2

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.