A note on global well-posedness and blow-up of some semilinear evolution equations

Tarek Saanouni

doi:10.3934/eect.2015.4.355

Article Contents

2015, Volume 4, Issue 3: 355-372. Doi: 10.3934/eect.2015.4.355

This issue Previous Article A backward uniqueness result for the wave equation with absorbing boundary conditions Next Article

A note on global well-posedness and blow-up of some semilinear evolution equations

Tarek Saanouni^1,

1.
University Tunis El Manar, Faculty of Sciences of Tunis, Department of Mathematics, 2092, Tunis

Received: December 31, 2014

Revised: June 30, 2015

Published: August 2015

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Abstract

We investigate the initial value problems for some semilinear wave, heat and Schrödinger equations in two space dimensions, with exponential nonlinearities. 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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Mathematics Subject Classification: Primary: 35Q55.

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