UTA Department of Mathematics

Applied Mathematics Seminar

Date/Time/Room: Friday (03/28/2003) at 2:00pm in 304 Pickard Hall

Speaker: Theresa Jorgensen, Department of Mathematics, University of Texas at Arlington

"Global Regularity for Nonlinear Wave Equations"

Abstract: We consider an initial-boundary value problem for a nonlinear wave equation in one space dimension. The equation is a particular case of a more general evolution equation which arises in physics, for example, in quantum field theory and in a model for a classical vibrating membrane with a resistance force that is proportional to the velocity. The nonlinearity we study features competing damping and source terms. It is well known that when the damping term is absent from the equation, then the source term drives the solution to blow up in finite time. However, the interaction between the damping and source terms is often difficult to analyze. We determine simple conditions which control the global existence and nonexistence of solutions, regardless of the size of the initial data.