scholarly journals On the Cauchy problem for a degenerate parabolic differential equation

1998 ◽  
Vol 21 (3) ◽  
pp. 555-558
Author(s):  
Ahmed El-Fiky
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Parabolic Equation ◽  
Degenerate Parabolic Equation ◽  
Parabolic Differential Equation ◽  
The Cauchy Problem ◽  
Uniqueness Of The Solution ◽  
Degenerate Parabolic

The aim of this work is to prove the existence and the uniqueness of the solution of a degenerate parabolic equation. This is done using H. Tanabe and P.E. Sobolevsldi theory.

LOCALIZATION OF SOLUTIONS TO A DOUBLY DEGENERATE PARABOLIC EQUATION WITH A STRONGLY NONLINEAR SOURCE

2012 ◽  
Vol 14 (03) ◽  
pp. 1250018 ◽  
Author(s):  
CHUNLAI MU ◽  
PAN ZHENG ◽  
DENGMING LIU
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Initial Data ◽  
Compact Support ◽  
Degenerate Parabolic Equation ◽  
Nonlinear Source ◽  
Strongly Nonlinear ◽  
The Cauchy Problem ◽  
Degenerate Parabolic

In this paper, we investigate the localization of solutions of the Cauchy problem to a doubly degenerate parabolic equation with a strongly nonlinear source [Formula: see text] where N ≥ 1, p > 2 and m, l, q > 1. When q > l + m(p - 2), we prove that the solution u(x, t) has strict localization if the initial data u0(x) has a compact support, and we also show that the solution u(x, t) has the property of effective localization if the initial data u0(x) satisfies radially symmetric decay. Moreover, when 1 < q < l + m(p - 2), we obtain that the solution of the Cauchy problem blows up at any point of RNto arbitrary initial data with compact support.

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