Nonlinear parabolic and elliptic equations. (English) Zbl 0777.35001

Pao, Chia-Ven

New York: Plenum Press. xv, 777 p. (1992).

The book considers nonlinear parabolic and elliptic problems, also of integro-differential type or with integral boundary conditions. The book is focused on applications to reaction-diffusion problems and the method most frequently used to prove existence of a solution is the method of upper-lower solutions with monotone iterations. An extensive discussion is also given to stability and blow-up of time depending solutions. The problems are not only considered in bounded sets and a chapter is devoted to the study of problems in unbounded sets.
The book is divided into twelve chapters. The first seven chapters are devoted to the scalar case and the last five chapters are concerned with coupled systems. Various applications in particular to systems arising in biology, ecology, biochemistry, heat mass transfer, neutron transport and engineering are considered.

Reviewer: M.Biroli (Monza)

MSC:

35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations
35J60	Nonlinear elliptic equations
35K55	Nonlinear parabolic equations
35K57	Reaction-diffusion equations

Keywords:

nonlinear elliptic equations; nonlinear parabolic equations; reaction- diffusion systems; upper-lower solutions; stability; blow-up; bounded sets; unbounded sets