Harnac inequalities integral representation, and fatou theorem for classical positive solutions of parabolic equations with weight 2(2q + 1)

1979 ◽  
Vol 30 (4) ◽  
pp. 384-390
Author(s):  
S. D. �idel'man ◽  
T. G. Pletneva
Keyword(s):  
Integral Representation ◽  
Positive Solutions ◽  
Parabolic Equations ◽  
Fatou Theorem

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 The uniqueness of positive solutions of parabolic equations of divergence form on an unbounded domain

1993 ◽  
Vol 130 ◽  
pp. 111-121 ◽  
Author(s):  
Masaharu Nishio
Keyword(s):  
Euclidean Space ◽  
Positive Solutions ◽  
Unbounded Domain ◽  
Parabolic Equations ◽  
Divergence Form ◽  
Dimensional Euclidean Space

Let Rn+1 = Rn × R be the (n + 1)-dimensional Euclidean space (n ≥ 1). For X ∈ Rn+1, we write X = (x, t) with x ∈ Rn and t ∈ R. We consider parabolic operators of the following form:(1)

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