Local and non-local boundary quenching

✍ Scribed by Catherine A. Roberts; W. E. Olmstead

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 149 KB
• Volume: 22
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(19991110)22:16<1465::aid-mma88>3.0.co;2-#

✦ Synopsis

The quenching problem is examined for a one-dimensional heat equation with a non-linear boundary condition that is of either local or non-local type. Su$cient conditions are derived that establish both quenching and non-quenching behaviour. The growth rate of the solution near quenching is also given for a power-law non-linearity. The analysis is conducted in the context of a nonlinear Volterra integral equation that is equivalent to the initial}boundary value problem.