EXISTENCE AND EXPONENTIAL DECAY ESTIMATES FOR A SYSTEM OF NONLINEAR WAVE EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

L. T. P. Ngoc, T. M. Thuyet, H. N. Ky, N. T. Long

Abstract


The paper is devoted to the study of a system of nonlinear equations with nonlin-
ear boundary conditions. First, based on Faedo-Galerkin method and standard arguments of
density corresponding to the regularity of initial conditions, we establish two global existence
theorems of weak solutions. Next, the exponential decay property of the global solution via
the construction of a suitable Lyapunov functional is presented.

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ISSN: 1229-1595 (Print), 2466-0973 (Online)