Evolution Equations and Control Theory (EECT)

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

Pages: 355 - 372, Volume 4, Issue 3, September 2015      doi:10.3934/eect.2015.4.355

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Tarek Saanouni - University Tunis El Manar, Faculty of Sciences of Tunis, Department of Mathematics, 2092, Tunis, Tunisia (email)

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.

Keywords:  Nonlinear wave equation, nonlinear heat equation, nonlinear Schrödinger equation, global existence, blow-up, ground state.
Mathematics Subject Classification:  Primary: 35Q55.

Received: January 2015;      Revised: July 2015;      Available Online: September 2015.