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New problems in stability of viscous shock waves
PDE Seminar| Speaker: | Kevin Zumbrun, Indiana University |
| Location: | 3106 MSB |
| Start time: | Mon, May 14 2007, 4:10PM |
Description
Recent progress has reduced the study of nonlinear time-evolutionary
stability of viscous shock waves to determination of spectral stability,
or location of eigenvalues of the linearized operator about the wave:
that is, from a rather stiff PDE initial value problem to an ODE
boundary-value
problem that is analytically and numerically well conditioned. However,
the resulting ODE are variable-coefficient and dimension three or higher,
so challenging in their own right. Their study presents a new array of
problems
rather different from those of the preceding theory. We discuss general
strategies for their solution combining numerical methods with methods from
asymptotic ode/singular perturbation theory, and give specific examples
indicating their use.