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- Title
On the existence and nonexistence of solutions of some quasilinear hyperbolic equations.
- Authors
Pokhozhaev, S.
- Abstract
We consider a special class of quasilinear hyperbolic equations of arbitrary order suggested by V.A. Galaktionov. For these equations, we prove the existence of solutions periodic in t > 0 and consider an initial-boundary value problem for which we derive sufficient conditions for the nonexistence of a global solution in the natural energy space of solutions.
- Subjects
HYPERBOLIC differential equations; QUASILINEARIZATION; GALAKTIONOV, V. A.; BOUNDARY value problems; INITIAL value problems
- Publication
Differential Equations, 2011, Vol 47, Issue 12, p1754
- ISSN
0012-2661
- Publication type
Article
- DOI
10.1134/S0012266111120056