On positive solutions of semilinear periodic-parabolic problems

1984 ◽  
pp. 101-114 ◽  
Author(s):  
P. Hess
Keyword(s):  
Positive Solutions ◽  
Parabolic Problems

scholarly journals Life Span of Positive Solutions for the Cauchy Problem for the Parabolic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Yusuke Yamauchi
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Life Span ◽  
Recent Result ◽  
Positive Solutions ◽  
Parabolic Equations ◽  
Blow Up ◽  
Parabolic Problems ◽  
Survey Paper ◽  
The Cauchy Problem

Since 1960's, the blow-up phenomena for the Fujita type parabolic equation have been investigated by many researchers. In this survey paper, we discuss various results on the life span of positive solutions for several superlinear parabolic problems. In the last section, we introduce a recent result by the author.

scholarly journals A priori bounds and complete blow-up of positive solutions of indefinite superlinear parabolic problems

2005 ◽  
Vol 304 (2) ◽  
pp. 614-631 ◽  
Author(s):  
Pavol Quittner ◽  
Frédérique Simondon
Keyword(s):  
Positive Solutions ◽  
Blow Up ◽  
A Priori ◽  
Parabolic Problems ◽  
A Priori Bounds

Positive solutions for sublinear periodic parabolic problems

2003 ◽  
Vol 55 (1-2) ◽  
pp. 73-82
Author(s):  
T. Godoy ◽  
U. Kaufmann ◽  
S. Paczka
Keyword(s):  
Positive Solutions ◽  
Parabolic Problems

scholarly journals On the existence of positive solutions for periodic parabolic sublinear problems

2003 ◽  
Vol 2003 (17) ◽  
pp. 975-984 ◽  
Author(s):  
T. Godoy ◽  
U. Kaufmann
Keyword(s):  
Bounded Domain ◽  
Positive Solutions ◽  
Wide Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Parabolic Problems ◽  
Smooth Bounded Domain ◽  
Carathéodory Functions ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for the existence of positive solutions for sublinear Dirichlet periodic parabolic problemsLu=g(x,t,u)inΩ×ℝ(whereΩ⊂ℝNis a smooth bounded domain) for a wide class of Carathéodory functionsg:Ω×ℝ×[0,∞)→ℝsatisfying some integrability and positivity conditions.

Blow-up Results for Parabolic Inequalities with Chipot–Weissler Nonlinearity in the Gradient Term

2004 ◽  
Vol 4 (2) ◽  
Author(s):  
Anna Maria Piccirillo ◽  
Luisa Toscano ◽  
Speranza Toscano
Keyword(s):  
Positive Solutions ◽  
Wide Class ◽  
Blow Up ◽  
Parabolic Problems ◽  
Gradient Term ◽  
Nonlinear Parabolic Problems ◽  
Nonlinear Parabolic ◽  
Open Question ◽  
Parabolic Inequalities

AbstractWe obtain blow-up results for a wide class of nonlinear parabolic problems with nonlinearity of the Chipot-Weissler type in the gradient term. Some of these answer an open question concerning the nonexistence of positive solutions to the problemwhere λ > 0 is small, u

scholarly journals The symmetry of positive solutions of periodic-parabolic problems

1994 ◽  
Vol 52 (1-3) ◽  
pp. 81-89 ◽  
Author(s):  
E.N. Dancer ◽  
P. Hess
Keyword(s):  
Positive Solutions ◽  
Parabolic Problems

Positive solutions for a quasilinear system Via blow up

1993 ◽  
Vol 18 (12) ◽  
pp. 2071-2106
Author(s):  
Philippe Clément ◽  
Raúl Manásevich ◽  
Enzo Mitidieri
Keyword(s):  
Positive Solutions ◽  
Blow Up ◽  
Quasilinear System
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