The Cauchy problem for a degenerate parabolic equation with inhomogeneous density and source in the class of slowly decaying initial data

2012 ◽  
Vol 76 (3) ◽  
pp. 563-580 ◽  
Author(s):  
Aleksandr V Martynenko ◽  
Anatoli F Tedeev ◽  
Vladimir N Shramenko
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Initial Data ◽  
Degenerate Parabolic Equation ◽  
The Cauchy Problem ◽  
Inhomogeneous Density ◽  
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 Doubly Degenerate Parabolic Equation with Time-Dependent Gradient Source and Initial Data Measures

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Lihua Deng ◽  
Xianguang Shang
Keyword(s):  
Parabolic Equation ◽  
Initial Data ◽  
Degenerate Parabolic Equation ◽  
A Priori Estimates ◽  
A Priori ◽  
Local Existence ◽  
Time Dependent ◽  
Priori Estimates ◽  
The Cauchy Problem ◽  
Degenerate Parabolic

This paper is devoted to the Cauchy problem for a class of doubly degenerate parabolic equation with time-dependent gradient source, where the initial data are Radon measures. Using the delicate a priori estimates, we first establish two local existence results. Furthermore, we show that the existence of solutions is optimal in the class considered here.

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.

Sign in / Sign up

Export Citation Format

Share Document