Convergence of One-Parameter Operator Semigroups : In Models of Mathematical Biology and Elsewhere (Hardcover)

Preface; 1. Semigroups of operators; Part I. Regular Convergence: 2. The first convergence theorem; 3. Example - boundary conditions; 4. Example - a membrane; 5. Example - sesquilinear forms; 6. Uniform approximation of semigroups; 7. Convergence of resolvents; 8. (Regular) convergence of semigroups; 9. Example - a queue; 10. Example - elastic boundary; 11. Example - membrane again; 12. Example - telegraph; 13. Example - Markov chains; 14. A bird's-eye view; 15. Hasegawa's condition; 16. Blackwell's example; 17. Wright's diffusion; 18. Discrete-time approximation; 19. Discrete-time approximation - examples; 20. Back to Wright's diffusion; 21. Kingman's n-coalescent; 22. The Feynman?Kac formula; 23. The two-dimensional Dirac equation; 24. Approximating spaces; 25. Boundedness, stablization; Part II. Irregular Convergence: 26. First examples; 27. Example - genetic drift; 28. The nature of irregular convergence; 29. Convergence under perturbations; 30. Stein's model; 31. Uniformly holomorphic semigroups; 32. Asymptotic behavior of semigroups; 33. Fast neurotransmitters; 34. Fast neurotransmitters II; 35. Diffusions on graphs and Markov chains; 36. Semilinear equations; 37. Coagulation-fragmentation equation; 38. Homogenization theorem; 39. Shadow systems; 40. Kinases; 41. Uniformly differentiable semigroups; 42. Kurtz's theorem; 43. A singularly perturbed Markov chain; 44. A Tikhonov-type theorem; 45. Fast motion and frequent jumps; 46. Gene regulation and gene expression; 47. Some non-biological models; 48. Convex combinations of generators; 49. Dorroh and Volkonskii theorems; 50. Convex combinations in biology; 51. Recombination; 52. Recombination (continued); 53. Khasminskii's example; 54. Comparing semigroups; 55. Asymptotic analysis; 56. Greiner's theorem; 57. Fish dynamics; 58. Emergence of transmission conditions; 59. Emergence of transmission conditions II; Part III. Convergence of Cosine Families: 60. Regular convergence; 61. Cosines converge in a regular way; Part IV. Appendices: 62. Laplace transform; 63. Measurability implies continuity; References; Index.