The Gierer-Meinhardt system in various settings.

Tse, Wang Hung.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 75-77).Abstract also in Chinese.Chapter 1 --- Introduction --- p.1Chapter 2 --- On bounded interval with n jumps in inhibitor diffusivity --- p.3Chapter 2.1 --- Introduction --- p.3Chapter 2.2 --- Preliminaries --- p.5Chapter 2.3 --- Review of previous results in the two segment case: interior spike and spike near the jump discontinuity of the diffusion coefficient --- p.7Chapter 2.4 --- The construction and analysis of spiky steady-state solutions --- p.9Chapter 2.5 --- Stability Analysis --- p.10Chapter 2.6 --- Spikes near the jump discontinuity xb of the inhibitor diffusivity --- p.11Chapter 2.7 --- Stability Analysis II: Small Eigenvalues of the Spike near the Jump --- p.16Chapter 2.8 --- Existence of interior spikes for N segments --- p.20Chapter 2.9 --- Existence of a spike near a jump for N segments --- p.24Chapter 2.10 --- Appendix: The Green´ةs function for three segments --- p.25Chapter 3 --- On a compact Riemann surface without boundary --- p.30Chapter 3.1 --- Introduction --- p.30Chapter 3.2 --- Some Preliminaries --- p.35Chapter 3.3 --- Existence --- p.43Chapter 3.4 --- Refinement of Approximate Solution --- p.50Chapter 3.5 --- Stability --- p.52Chapter 3.6 --- Appendix I: Expansion of the Laplace-Beltrami Operator --- p.67Chapter 3.7 --- Appendix II: Some Technical Calculations --- p.7