𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Blow-up phenomena for a class of quasilinear parabolic problems under Robin boundary condition

✍ Scribed by Cristian Enache

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
237 KB
Volume
24
Category
Article
ISSN
0893-9659

No coin nor oath required. For personal study only.

✦ Synopsis

This note deals with a class of heat emission processes in a medium with a non-negative source, a nonlinear decreasing thermal conductivity and a linear radiation (Robin) boundary condition. For such heat emission problems, we make use of a first-order differential inequality technique to establish conditions on the data sufficient to guarantee that the blow-up of the solutions does occur or does not occur. In addition, the same technique is used to determine a lower bound for the blow-up time when blow-up occurs.

πŸ“œ SIMILAR VOLUMES

Blow-up solutions and global solutions f
Blow-up solutions and global solutions for a class of quasilinear parabolic equations with robin boundary conditions
✍ Juntang Ding; Shengjia Li πŸ“‚ Article πŸ“… 2005 πŸ› Elsevier Science 🌐 English βš– 506 KB

The type of problem under consideration is where D is a smooth bounded domain of R N, By constructing an auxiliary function and using Hopf's maximum principles on it, existence theorems of blow-up solutions, upper bound of "blow-up time", upper estimates of "blow-up rate", existence theorems of glo

Blow up, decay bounds and continuous dep
Blow up, decay bounds and continuous dependence inequalities for a class of quasilinear parabolic problems
✍ L. E. Payne; G. A. Philippin; S. Vernier-Piro πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 130 KB

## Abstract This paper deals with a class of semilinear parabolic problems. In particular, we establish conditions on the data sufficient to guarantee blow up of solution at some finite time, as well as conditions which will insure that the solution exists for all time with exponential decay of the

Blow-up, global existence and exponentia
Blow-up, global existence and exponential decay estimates for a class of quasilinear parabolic problems
✍ C. Enache πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 299 KB

This paper deals with a class of nonlinear parabolic problems in divergence form whose solutions, without appropriate data restrictions, might blow up at some finite time. The purpose of this paper is to establish conditions on the data sufficient to guarantee blow-up of solution at some finite time