EECT
A note on global well-posedness and blow-up of some semilinear evolution equations
Tarek Saanouni
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: ground state. global existence nonlinear heat equation blow-up Nonlinear wave equation nonlinear Schrödinger equation
CPAA
Global well-posedness of some high-order semilinear wave and Schrödinger type equations with exponential nonlinearity
Tarek Saanouni
Extending previous works [47, 27, 30], we consider in even space dimensions the initial value problems for some high-order semi-linear wave and Schrödinger type equations with exponential nonlinearity. We obtain global well-posedness in the energy space.
keywords: high-order Schrödinger type equation High-order wave type equation Moser-Trudinger inequality well-posedness. energy estimate

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