In this work we present some of the general theory of shock waves and their stability properties. We examine the concepts of nonlinear stability and spectral stability, noting that for certain classes of equations the study of nonlinear stability is reduced to the analysis of the spectra of the linearized eigenvalue problem. A useful tool in the study of spectral stability is the Evans function, an analytic function whose zeros correspond to the eigenvalues of the linearized eigenvalue problem. We discuss techniques for numerical Evans function computation that ensure analyticity, allowing standard winding number arguments and rootfinding methods to be used to locate eigenvalues. The Evans function is then used to study the spectra of the high Lewis number combustion system, tracking eigenvalues in the right-half plane.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Lytle, Joshua W., "Stability for Traveling Waves" (2011). All Theses and Dissertations. 3063.
traveling waves, nonlinear stability, spectral stability, Lewis number, combustion