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Remarks on the qualitative behavior of the undamped Klein‐Gordon equation
Author(s) -
EsquivelAvila Jorge A.
Publication year - 2017
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.4598
Subject(s) - mathematics , bounded function , mathematical analysis , dirichlet boundary condition , boundary value problem , klein–gordon equation , homogeneous , partial differential equation , supercritical fluid , nonlinear system , physics , quantum mechanics , combinatorics , thermodynamics
We consider the undamped Klein‐Gordon equation in bounded domains with homogeneous Dirichlet boundary conditions. For any real value of the initial energy, particularly for supercritical values of the energy, we give sufficient conditions to conclude blow‐up in finite time of weak solutions. The success of the analysis is based on a detailed analysis of a differential inequality. Our results improve previous ones in the literature.