Remarks on the qualitative behavior of the undamped Klein-Gordon equation

Esquivel-Avila, Jorge A.

  • Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 221-228

Abstract

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We present sufficient conditions on the initial data of an undamped Klein-Gordon equation in bounded domains with homogeneous Dirichlet boundary conditions to guarantee the blow up of weak solutions. Our methodology is extended to a class of evolution equations of second order in time. As an example, we consider a generalized Boussinesq equation. Our result is based on a careful analysis of a differential inequality. We compare our results with the ones in the literature.

How to cite

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Esquivel-Avila, Jorge A.. "Remarks on the qualitative behavior of the undamped Klein-Gordon equation." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 221-228. <http://eudml.org/doc/294881>.

@inProceedings{Esquivel2017,
abstract = {We present sufficient conditions on the initial data of an undamped Klein-Gordon equation in bounded domains with homogeneous Dirichlet boundary conditions to guarantee the blow up of weak solutions. Our methodology is extended to a class of evolution equations of second order in time. As an example, we consider a generalized Boussinesq equation. Our result is based on a careful analysis of a differential inequality. We compare our results with the ones in the literature.},
author = {Esquivel-Avila, Jorge A.},
booktitle = {Proceedings of Equadiff 14},
keywords = {Klein-Gordon equation, Blow up, High energies, Abstract wave equation, Generalized Boussinesq equation},
location = {Bratislava},
pages = {221-228},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {Remarks on the qualitative behavior of the undamped Klein-Gordon equation},
url = {http://eudml.org/doc/294881},
year = {2017},
}

TY - CLSWK
AU - Esquivel-Avila, Jorge A.
TI - Remarks on the qualitative behavior of the undamped Klein-Gordon equation
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 221
EP - 228
AB - We present sufficient conditions on the initial data of an undamped Klein-Gordon equation in bounded domains with homogeneous Dirichlet boundary conditions to guarantee the blow up of weak solutions. Our methodology is extended to a class of evolution equations of second order in time. As an example, we consider a generalized Boussinesq equation. Our result is based on a careful analysis of a differential inequality. We compare our results with the ones in the literature.
KW - Klein-Gordon equation, Blow up, High energies, Abstract wave equation, Generalized Boussinesq equation
UR - http://eudml.org/doc/294881
ER -

References

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