Abstract
AbstractUnder the acoustic boundary conditions, the initial boundary value problem of a wave equation with multiple nonlinear source terms is considered. This paper gives the energy functional of regular solutions for the wave equation and proves the decreasing property of the energy functional. Firstly, the existence of a global solution for the wave equation is proved by the Faedo–Galerkin method. Then, in order to obtain the nonexistence of global solutions for the wave equation, a new functional is defined. When the initial energy is less than zero, the special properties of the new functional are proved by the method of contraction. Finally, the conditions for the nonexistence of global solutions of the wave equation with acoustic boundary conditions are analyzed by using these special properties.
Funder
the Key Projects of Natural Science Research in Colleges and Universities of Anhui Province
the Key Scientific Research Projects of Suzhou University
the Research Projects of Anhui Education Department
the Scientific Research Platform Projects of Suzhou University
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
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