Wave equations and reaction-diffusion equations with several nonlinear source terms
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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.
Key wordswave equations reaction-diffusion equations potential wells global existence nonexistence
Chinese Library ClassificationO175.26 O175.27
2000 Mathematics Subject Classification35L70 35K57
- Lions J L. Quelques méthodes de résolution des problémes aux limites non linéaires[M]. Paris: Dunod Gauthier-Villars, 1969.Google Scholar