Abstract
The initial boundary value problem of wave equations and reaction-diffusion equations with several nonlinear source terms in a bounded domain is studied by potential well method. The invariance of some sets under the flow of these problems and the vacuum isolation of solutions are obtained by introducing a family of potential wells. Then the threshold result of global existence and nonexistence of solutions are given. Finally, the problem with critical initial conditions are discussed.
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Communicated by GUO Xing-ming
Project supported by the National Natural Science Foundation of China (No. 10271034) and the Basic Research Foundation of Harbin Engineering University (No. HEUF04012)
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Liu, Yc., Xu, Rz. & Yu, T. Wave equations and reaction-diffusion equations with several nonlinear source terms. Appl Math Mech 28, 1209–1218 (2007). https://doi.org/10.1007/s10483-007-0909-y
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DOI: https://doi.org/10.1007/s10483-007-0909-y