Concentrated patterns in biological systems [Elektronische Ressource] / vorgelegt von Matthias Winter

Concentrated Patterns in BiologicalSystemsVon der Fakultat Mathematik und Physik derUniversitat Stuttgart als Habilitationsschriftgenehmigte AbhandlungVorgelegt vonDr. Matthias Wintergeboren in Neuenstadt am KocherGutachter:Prof. Dr. Arjen DoelmanProf. Dr. Messoud EfendievProf. Dr. Karl-Peter HadelerProf. Dr. Alexander MielkeFachbereich Mathematik2003Key words and phrases. Concentration Phenomena, Gierer-MeinhardtSystem, Mathematical Biology, Pattern Formation, Singular Perturbation,Elliptic SystemsContentsChapter 1. Introduction 5Chapter 2. Preliminaries 171. Two linear operators in half space 172. Calculating the heights of the spikes 19Chapter 3. Existence 231. Construction of the Approximate Solutions 232. The Liapunov-Schmidt Reduction Method 313. The Reduced Problem 39Chapter 4. Stability 471. The Large Eigenvalues 472. The Small Eigenvalues 54Chapter 5. Appendices 651. Appendix A 652. Appendix B 703. Appendix C 744. Appendix D 785. Appendix E 82Chapter 6. Discussion 851. Discussion 85Bibliography 873CHAPTER 1IntroductionThis thesis is concerned with pattern formation in biological systems, inparticular those having the property that they concentrate at a boundarypoint in a bounded smooth domain.We study this problem within the framework of deterministic reaction-di usion systems.