8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology

Chapters in this book

1. Frontmatter i
2. Preface vii
3. Contents ix
4. 1 Introduction
5. 1.1 Scientific Frontiers at the Interface of Mathematics and Life Sciences 3
6. 2 Mathematical and Statistical Modeling of Biological Systems
7. 2.1 Ensemble Modeling of Biological Systems 19
8. 3 Probabilistic Models for Nonlinear Processes and Biological Dynamics
9. 3.1 Nonlinear Lévy and Nonlinear Feller Processes: an Analytic Introduction 45
10. 4 New Results in Mathematical Epidemiology and Modeling Dynamics of Infectious Diseases
11. 4.1 Formal Solutions of Epidemic Equation 73
12. 5 Mathematical Analysis of PDE-based Models and Applications in Cell Biology
13. 5.1 Asymptotic Analysis of the Dirichlet Spectral Problems in Thin Perforated Domains with Rapidly Varying Thickness and Different Limit Dimensions 89
14. 6 Axiomatic Modeling in Life Sciences with Case Studies for Virus-immune System and Oncolytic Virus Dynamics
15. 6.1 AxiomaticModeling in Life Sciences 113
16. 7 Theory, Applications, and Control of Nonlinear PDEs in Life Sciences
17. 7.1 On One Semilinear Parabolic Equation of Normal Type 147
18. 7.2 On some Classes of Nonlinear Equations with L¹-Data 161
19. 8 Mathematical Models of Pattern Formation and Their Applications in Developmental Biology
20. 8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology 191
21. 9 Modeling the Dynamics of Genetic Mechanism, Pattern Formation, and the Genetics of “Geometry”
22. 9.1 Modeling the Positioning of Trichomes on the Leaves of Plants 215
23. 10 Statistical Modeling in Life Sciences and Direct Measurements
24. 10.1 Error Estimation for Direct Measurements in May–June 1986 of ¹³¹I Radioactivity in Thyroid Gland of Children and Adolescents and Their Registration in Risk Analysis 231
25. 11 Design and Development of Experiments for Life Science Applications
26. 11.1 Physiological Effects of Static Magnetic Field Exposure in an in vivo Acute Visceral Pain Model in Mice 247
27. 12 Mathematical Biomedicine and Modeling Avascular Tumor Growth
28. 12.1 Continuum Models of Avascular Tumor Growth 279
29. Index 313