Displaying similar documents to “Weak solutions to the initial boundary value problem for a semilinear wave equation with damping and source terms”

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.

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.

Waves of excitations in heterogeneous annular region II. Strong asymmetry

Kristóf Kály-Kullai, András Volford, Henrik Farkas (2003)

Banach Center Publications

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Excitation wave propagation in a heterogeneous medium around a circular obstacle is investigated, when the obstacle is located very eccentrically with respect to the interfacial circle separating the slow inner and the fast outer region. Qualitative properties of the permanent wave fronts are described, and the calculated wave forms are presented.

The wave map problem. Small data critical regularity

Igor Rodnianski (2005-2006)

Séminaire Bourbaki

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The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is ( 2 + 1 ) , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory....