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Start Over Author "HAMCHI, ILHEM" Journal electronic journal of differential equations

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1. EXISTENCE AND BLOW UP IN A SYSTEM OF WAVE EQUATIONS WITH NONSTANDARD NONLINEARITIES.

Author

MESSAOUDI, SALIM A., BOUHOUFANI, OULIA, HAMCHI, ILHEM, and ALAHYANE, MOHAMED

Subjects
*WAVE equation, *NONLINEAR equations, *EXISTENCE theorems, *BLOWING up (Algebraic geometry), *NONLINEAR systems, *ENERGY consumption, *LYAPUNOV exponents
Abstract

In this article, we consider a coupled system of two nonlinear hyperbolic equations, where the exponents in the damping and source terms are variables. First, we prove a theorem of existence and uniqueness of weak solution, by using the Faedo Galerkin approximations and the Banach fixed point theorem. Then, using the energy method, we show that certain solutions with positive initial energy blow up in finite time. We also give some numerical applications to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Published
2021

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