Displaying similar documents to “Blow-Up of solutions to nonlinear wave equations in two space dimensions.”

Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping

Lorena Bociu, Irena Lasiecka (2008)

Applicationes Mathematicae

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We focus on the blow-up in finite time of weak solutions to the wave equation with interior and boundary nonlinear sources and dissipations. Our central interest is the relationship of the sources and damping terms to the behavior of solutions. We prove that under specific conditions relating the sources and the dissipations (namely p > m and k > m), weak solutions blow up in finite time.

On the nonlinear stabilization of the wave equation

Aissa Guesmia (1998)

Annales Polonici Mathematici

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We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.