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Blowup and decay behavior of solutions to the generalized Boussinesq‐type equation with strong damping
Author(s) -
Mohammadi Hamideh B.,
Esfahani Amin
Publication year - 2019
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.5556
Subject(s) - mathematics , initial value problem , type (biology) , mathematical analysis , cauchy distribution , space (punctuation) , property (philosophy) , cauchy problem , computer science , philosophy , epistemology , operating system , ecology , biology
In this paper, we study the Cauchy problem for the generalized Boussinesq‐type equation with strong damping. By defining a suitable solution space with time‐weighted norms and under smallness condition on the initial data, we establish the global existence and decay property of the solutions. Under certain conditions on the initial data, we also provide blowup of the solutions.