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Well‐posedness of nonlinear wave equation with combined power‐type nonlinearities
Author(s) -
Runzhang Xu,
Chuang Xu,
Yang Liu,
Tao Yu
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1408
Subject(s) - mathematics , nonlinear system , invariant (physics) , boundary value problem , type (biology) , mathematical analysis , initial value problem , wave equation , power (physics) , mathematical physics , physics , ecology , quantum mechanics , biology
In this paper, we study the initial boundary‐value problem with combined power‐type nonlinearities by utilizing potential well method. We provide an algorithm to compute the depth of the potential well with the help of Mathematica, and derive the invariant subsets, global existence and blowup of solutions. Moreover, we obtain the invariant subsets, global existence and blowup of solutions for the critical case. Copyright © 2011 John Wiley & Sons, Ltd.