Advances in Differential Equations

Type-II blowup for a semilinear heat equation

Noriko Mizoguchi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


The present paper is concerned with a Cauchy problem for a semilinear heat equation, \[ \left\{ \begin{array}{ll} u_t = \Delta u + u^p & \quad \mbox{ in } {{\bf R}}^N \times (0,\infty), \hspace{3.5cm}\\ u(x,0) = u_0(x) \geq 0 & \quad \mbox{ in } {{\bf R}}^N. \end{array} \right. \tag*{(P)} \] A solution $ u $ of (P) is said to exhibit type-II blowup at $ t = T < + \infty $ if \[ \limsup_{ t \nearrow T } (T-t)^{ 1/(p-1) } |u(t)|_\infty = + \infty \] with the supremum norm $ | \cdot |_\infty $ in $ {{\bf R}}^N $. We show the existence of type-II-blowup solutions. Though our proof is based on the argument due to [9, 10], it is simpler than theirs by taking account of the number of intersections with the singular steady state of (P).

Article information

Adv. Differential Equations, Volume 9, Number 11-12 (2004), 1279-1316.

First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B40: Asymptotic behavior of solutions 35K15: Initial value problems for second-order parabolic equations 35K57: Reaction-diffusion equations


Mizoguchi, Noriko. Type-II blowup for a semilinear heat equation. Adv. Differential Equations 9 (2004), no. 11-12, 1279--1316.

Export citation