Systems of nonlinear partial differential equations. Applications to biology and engineering. (English) Zbl 0691.35002

Leung, Anthony W.

Mathematics and its applications, 49. Dordrecht etc.: Kluwer Academic Publishers. xiii, 409 p. Dfl. 190.00; £62.00; $ 99.00 (1989).

The aim of the book is to study some classes of nonlinear systems of elliptic and parabolic partial differential equations related to ecological systems, fission reactors, chemical reactors and many other applied topics. Its contents is: 1. Background and fundamental methods; 2. Interacting population reaction-diffusion systems; Dirichlet conditions; 3. Other boundary conditions, nonlinear diffusion, asymptotics; 4. Multigroup fission reactor systems; strongly order- preserving systems; 5. Monotone schemes for elliptic systems, periodic solutions; 6. Systems of finite difference equations; numerical solutions; 7. Large systems under Neumann boundary conditions, bifurcations, 8. Appendix.
Written by a leading specialist in the field and based mainly on the results obtained by the author, the book is an excellent guide in this subject as well as a source of inspiration for further investigations.
We recommend it to all interested in partial differential equations and its applications to biology and engineering.

Reviewer: I.A.Rus

MSC:

35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations
35K57	Reaction-diffusion equations
35J65	Nonlinear boundary value problems for linear elliptic equations
65M99	Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99	Numerical methods for partial differential equations, boundary value problems
35B32	Bifurcations in context of PDEs
35B40	Asymptotic behavior of solutions to PDEs
80A32	Chemically reacting flows
92B05	General biology and biomathematics

Keywords:

ecological systems; fission; Dirichlet conditions; Neumann boundary conditions; engineering