Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 0942.35025
Deng, Keng; Levine, Howard A.
The role of critical exponents in blow-up theorems: The sequel.
(English)
[J] J. Math. Anal. Appl. 243, No.1, 85-126 (2000). ISSN 0022-247X

Consider the Cauchy problem in $\Bbb R^N$ for the equation $u_t=\Delta u+u^p$, where $p>1$ and $u\geq 0$. In 1966, {\it H. Fujita} [J. Fac. Sci., Univ. Tokyo, Sect. I 13, 109-124 (1966; Zbl 0163.34002)] showed that this problem does not have global nontrivial solutions if $p<p_c:=1+2/N$ whereas both global and non-global positive solutions exist if $p>p_c$. The exponent $p_c$ is called Fujita's critical exponent. The authors discuss various Fujita-type results which have appeared in the literature since 1990. These results include degenerate equations, problems in unbounded domains and on manifolds, problems with inhomogeneous boundary conditions, cooperative systems of equations. Moreover, the paper contains a section with open problems.
[P.Quittner (Bratislava)]
MSC 2000:
*35B33 Critical exponents
35K55 Nonlinear parabolic equations
35B35 Stability of solutions of PDE
35B40 Asymptotic behavior of solutions of PDE

Keywords: degenerate equations; global existence; problems in unbounded domains and on manifolds; inhomogeneous boundary conditions; cooperative systems

Citations: Zbl 0163.34002

Cited in: Zbl 1074.35045

Highlights
Master Server