On the Damped Nonlinear Evolution Equation W Sub tt = Sigma (W)Sub xx - Gamma W Sub t.
Abstract
The damped nonlinear wave equation W(tt) = sigma(W)(xx) minus gamma W(T) is formally equivalent to a quasilinear system of the form (W(t) - V(x) = 0) and (V(t) minus sigma (W)(x) + gamma V = 0) which arises, in particular, in models of shearing flow in a nonlinear viscoelastic fluid. In such models, it has been shown that when the system is strictly hyperbolic, i.e., sigma primed (0) > 0 and the initial data is small (so that sigma primed (W) > 0 for as long as solutions exist) smooth solutions will fail to exist globally in time if the gradients of the initial data are too large. In this paper, we show that similar results hold if sigma primed (0) = 0 or if sigma primed (zeta) < 0 for absolute value of zeta sufficiently large; we also derive growth estimates for the L(2) norm of a maximally-defined smooth solution.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 30, 1981
- Accession Number
- ADA095866
Entities
People
- Frederick Bloom
Organizations
- University of South Carolina