The Blow-up Rate for a System of Heat Equations with Non-trivial Coupling at the Boundary

✍ Scribed by Julio D. Rossi

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 222 KB
• Volume: 20
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(19970110)20:1<1::aid-mma843>3.0.co;2-e

✦ Synopsis

Under some natural hypothesis on the matrix P"(p GH ) that guarrantee the blow-up of the solution at time ¹, and some assumptions of the initial data u G , we find that if "" x """1 then u G (x , t)goestoinfinitylike(¹!t) G /2 , where the G (0 are the solutions of (P!Id) ( , )R"(!1, !1)R. As a corollary of the blow-up rate we obtain the loclaization of the blow-up set at the boundary of the domain.

-----* Supported by Universidad de Buenos Aires under grant EX071 and Conicet.