Displaying similar documents to “Local Existence of Weak Solutions to the Quasi-Linear Wave Equation for Large Initial Values.”

Weak solutions to the initial boundary value problem for a semilinear wave equation with damping and source terms

Petronela Radu (2008)

Applicationes Mathematicae

Similarity:

We show local existence of solutions to the initial boundary value problem corresponding to a semilinear wave equation with interior damping and source terms. The difficulty in dealing with these two competitive forces comes from the fact that the source term is not a locally Lipschitz function from H¹(Ω) into L²(Ω) as typically assumed in the literature. The strategy behind the proof is based on the physics of the problem, so it does not use the damping present in the equation. The...

On the quasi-weak drop property

J. H. Qiu (2002)

Studia Mathematica

Similarity:

A new drop property, the quasi-weak drop property, is introduced. Using streaming sequences introduced by Rolewicz, a characterisation of the quasi-weak drop property is given for closed bounded convex sets in a Fréchet space. From this, it is shown that the quasi-weak drop property is equivalent to weak compactness. Thus a Fréchet space is reflexive if and only if every closed bounded convex set in the space has the quasi-weak drop property.