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 corol
On the blow-up rate for the heat equation with a nonlinear boundary condition
✍ Scribed by Miroslav Chlebík; Marek Fila
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 92 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0170-4214
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We study the boundedness and a priori bounds of global solutions of the problem u"0 in ;(0, ¹ ), j S j R # j S j "h(u) on j ;(0, ¹ ), where is a bounded domain in 1,, is the outer normal on j and h is a superlinear function. As an application of our results we show the existence of sign-changing sta
In this paper, following the ideas of Lax, we prove a blow-up result for a class of solutions of the equation & -&x -&+xx -= 0, corresponding, in certain cases, to the development of a singularity in the second derivatives of 4. These solutions solve locally (in time) the Cauchy problem for smooth i