Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1173.35531
Giga, Yoshikazu; Umeda, Noriaki
Blow-up directions at space infinity for solutions of semilinear heat equations. (English)
[J] Bol. Soc. Parana. Mat. (3) 23, No. 1-2, 9-28 (2005); correction ibid. 24, No. 1-2, 19-24 (2006). ISSN 0037-8712

The paper deals with a blowing up solution of the semilinear heat equation $$u_t=\Delta u+ f(u),\quad x \in \mathbb{R}^n,\ t>0 $$ with initial data $u_0$ satisfying $-N\leq u_0\leq M$, $u_0 \not\equiv M$ and $\lim_{|x|\to \infty} \inf_{x\in B_m} u_0(x)=M$, where $M+N>0$, $f(M)>0$ and radius of ball $B_m$ diverges to the infinity as $m\to \infty$. The nonlinear term $f$ is assumed to be Lipschitz in $\mathbb{R}$ and $\liminf_{s \to \infty}f(s)/s^p>0$ for some $p>1$, $f'\geq 0$. In the main result authors show that the solution blows up only at the space infinity. Furthermore, authors introduce a notion of blow up direction at the space infinity and establish characterizations for blow up directions by profile of initial data.
[Yavdat Ilyasov (Ufa)]

MSC 2000:: *35K55 Nonlinear parabolic equations
35K05 Heat equation
35K15 Second order parabolic equations, initial value problems
35B40 Asymptotic behavior of solutions of PDE
35B05 General behavior of solutions of PDE

Keywords: similinear heat equation; blow up; sub-super solution

Cited in: Zbl 1185.35116

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]