×

Some properties of solutions for a nonlinear diffusion system. I. (English) Zbl 0879.35068

Summary: We are concerned with the properties of BV solutions for a nonlinear diffusion system arising from dynamics of biological groups. We establish a comparison theorem and then show the uniqueness and nonuniqueness of solutions. Subsequently, we shall discuss in detail the extinction, blow-up, localization, and other properties of BV solutions in our following paper [reviewed below].

MSC:

35K45 Initial value problems for second-order parabolic systems
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35K55 Nonlinear parabolic equations
92D25 Population dynamics (general)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)

Citations:

Zbl 0879.35069
PDFBibTeX XMLCite