Mathematical Aspects of Reacting and Diffusing Systems

Häftad, Engelska, 1979

Del 28 i serien Lecture Notes in Biomathematics

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Beskrivning

Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. for example, the electric potential of a membrane can diffuse like a chemical, and of course can interact with real chemical species (ions) which are transported through the membrane.

Produktinformation

Utgivningsdatum:1979-03-05
Mått:170 x 244 x 17 mm
Vikt:354 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Biomathematics
Antal sidor:185
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540091172

Utforska kategorier

Tillämpad matematik inom Naturvetenskap och teknik

Innehållsförteckning

Preface and General Introduction.- 1. Modeling Considerations.- 1.1 Basic hypotheses.- 1.2 Redistribution processes.- 1.3 Boundaries and interfaces.- 1.4 Reactions with migration.- 1.5 The reaction mechanism.- 1.6 Positivity of the density.- 1.7 Homogeneous systems.- 1.8 Modeling the rate functions.- 1.9 Colony models.- 1.10 Simplifying the model by means of asymptotics.- 2. Fisher’s Nonlinear Diffusion Equation and Selection-Migration Models.- 2.1 Historical overview.- 2.2 Assumptions for the present model.- 2.3 Reduction to a simpler model.- 2.4 Comments on the comparison of models.- 2.5 The question of formal approximation.- 2.6 The case of a discontinuous carrying capacity.- 2.7 Discussion.- 3. Formulation of Mathematical Problems.- 3.1 The standard problems.- 3.2 Asymptotic states.- 3.3 Existence questions.- 4. The Scalar Case.- 4.1 Comparison methods.- 4.2 Derivative estimates.- 4.3 Stability and instability of stationary solutions.- 4.4 Traveling waves.- 4.5 Global stability of traveling waves.- 4.6 More on Lyapunov methods.- 4.7 Further results in the bistable case.- 4.8 Stationary solutions for x-dependent source function.- 5. Systems: Comparison Techniques.- 5.1 Basic comparison theorems.- 5.2 An example from ecology.- 6. Systems: Linear Stability Techniques.- 6.1 Stability considerations for nonconstant stationary solutions and traveling waves.- 6.2 Pattern stability for a class of model systems.- 7. Systems: Bifurcation Techniques.- 7.1 Small amplitude stationary solutions.- 7.2 Small amplitude wave trains.- 7.3 Bibliographical discussion.- 8. Systems: Singular Perturbation and Scaling Techniques.- 8.1 Fast wave trains.- 8.2 Sharp fronts (review).- 8.3 Slowly varying waves (review).- 8.4 Partitioning (review).- 8.5 Transient asymptotics.- 9. References toOther Topics.- 9.1 Reaction-diffusion systems modeling nerve signal propagation.- 9.2 Miscellaneous.- References.