Nonlinear wave equations and reaction-diffusion equations with several nonlinear source terms of different signs at high energy level

Runzhang Xu, Yanbing Yang, Shaohua Chen, Jia Su, Jihong Shen, Shaobin Huang

Abstract


This paper is concerned with the initial boundary value problem of a class of nonlinear wave equations and reaction–diffusion equations with several nonlinear source terms of different signs. For the initial boundary value problem of the nonlinear wave equations, we derive a blow up result for certain initial data with arbitrary positive initial energy. For the initial boundary value problem of the nonlinear reaction–diffusion equations, we discuss some probabilities of the existence and nonexistence of global solutions and give some sufficient conditions for the global and nonglobal existence of solutions at high initial energy level by employing the comparison principle and variational methods.

doi:10.1017/S1446181113000175

Keywords


wave equation, reaction–diffusion equation, high energy level, finite time blow-up, variational method, comparison principle



DOI: http://dx.doi.org/10.21914/anziamj.v54i0.6468



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.