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A NOTE ON GLOBAL WELL-POSEDNESS AND BLOW-UP OF SOME SEMILINEAR EVOLUTION EQUATIONS
Journal article   Open access  Peer reviewed

A NOTE ON GLOBAL WELL-POSEDNESS AND BLOW-UP OF SOME SEMILINEAR EVOLUTION EQUATIONS

Tarek Saanouni and University Tunis El Manar, Faculty of Sciences of Tunis, Department of Mathematics, 2092, Tunis
Evolution equations and control theory, Vol.4(3), pp.355-372
2015
DOI: https://doi.org/10.3934/eect.2015.4.355

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
We investigate the initial value problems for some semilinear wave, heat and Schrodinger equations in two space dimensions, with exponential non-linearities. Using the potential well method based on the concepts of invariant sets, we prove either global well-posedness or finite time blow-up.
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https://doi.org/10.3934/eect.2015.4.355View
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