Wave equations and reaction-diffusion equations with several nonlinear source terms

  • Liu Ya-cheng  (刘亚成)
  • Xu Run-zhang  (徐润章)Email author
  • Yu Tao  (于涛)


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 words

wave equations reaction-diffusion equations potential wells global existence nonexistence 

Chinese Library Classification

O175.26 O175.27 

2000 Mathematics Subject Classification

35L70 35K57 


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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Liu Ya-cheng  (刘亚成)
    • 1
  • Xu Run-zhang  (徐润章)
    • 1
    Email author
  • Yu Tao  (于涛)
    • 1
  1. 1.College of ScienceHarbin Engineering UniversityHarbinP. R. China

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