Thümmler, Vera: Numerical analysis of the method of freezing traveling waves. 2005
Content
- Contents
- Introduction
- Stability of traveling waves as PDAE solutions
- Stability with asymptotic phase
- The PDAE formulation
- The semilinear equation
- The linear inhomogenous equation
- Resolvent estimates
- Estimates of the solution operator
- Local existence and uniqueness
- Proof of the stability theorem
- Stability of relative equilibria
- Approximation via difference equations
- Resolvent estimates and approximation of eigenvalues
- Stability of the discretized system
- Numerical results
- Auxiliary results
- Functional analytic notions
- Fixed point theorems
- Exponential dichotomies for ordinary differential equations
- Notation
- List of Figures
- Bibliography