𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Global existence and finite time blow up for a degenerate reaction–diffusion system

✍ Scribed by Weibing Deng

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
222 KB
Volume
60
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

✦ Synopsis

This paper investigates the blow-up and global existence of solutions of the degenerate reactiondiffusion system

with homogeneous Dirichlet boundary data, where ⊂ R N is a bounded domain with smooth boundary * , m, n > 1, , 0 and p, q > 0. It is proved that if m > , n > and pq < (m -)(n -) every nonnegative solution is global, whereas if m < or n < or pq > (m -)(n -), there exist both global and blow up nonnegative solutions. When m > , n > and pq =(m-)(n-), we show that there exists * 1 which depends on the parameters p, q, m, n, , such that all positive solutions are global if 1 > * , while if 1 < 1/ * all positive solutions blow up in finite time, where 1 is the first Dirichlet eigenvalue for the Laplacian on .

📜 SIMILAR VOLUMES

Global existence and blow-up to a degene
Global existence and blow-up to a degenerate reaction–diffusion system with nonlinear memory
✍ Jun Zhou; Chunlai Mu; Mingshu Fan 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 266 KB

In this paper, we consider a degenerate reaction-diffusion system coupled by nonlinear memory. Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time. Furthermore, the blow-up rates are obtained.

Global and blow-up solutions for non-lin
Global and blow-up solutions for non-linear degenerate parabolic systems
✍ Zhi-wen Duan; Li Zhou 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 229 KB

## Abstract In this paper the degenerate parabolic system __u__~__t__~=__u__(__u__~__xx__~+__av__). __vt__=__v__(__v__~__xx__~+__bu__) with Dirichlet boundary condition is studied. For $a. b {<} \lambda\_{1} (\sqrt {ab} {<} \lambda\_{1} {\rm if}\, \alpha\_{1} {\neq} \alpha\_{2})$, the global existe