scholarly journals Cauchy Problem and Initial Trace for a Doubly Degenerate Parabolic Equation with Strongly Nonlinear Sources

2001 ◽  
Vol 264 (1) ◽  
pp. 49-67 ◽  
Author(s):  
Jing Li
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Degenerate Parabolic Equation ◽  
Strongly Nonlinear ◽  
Degenerate Parabolic

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.

scholarly journals Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Pan Zheng ◽  
Chunlai Mu ◽  
Dengming Liu ◽  
Xianzhong Yao ◽  
Shouming Zhou
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Degenerate Parabolic Equation ◽  
Blow Up ◽  
Single Point ◽  
Nonlinear Source ◽  
Strongly Nonlinear ◽  
Blow Up Analysis ◽  
The Cauchy Problem ◽  
Degenerate Parabolic

We investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear sourceut=div(|∇um|p−2∇ul)+uq,  (x,t)∈RN×(0,T), whereN≥1,p>2, andm,l,  q>1, and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and nonexistence of global solutions of the Cauchy problem. Moreover, under some suitable conditions we prove single-point blow-up for a large class of radial decreasing solutions.

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.

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