Stabilization of the solution of the Cauchy problem for a parabolic equation with bounded coefficients multiplying the solution gradient

2015 ◽  
Vol 91 (1) ◽  
pp. 47-49
Author(s):  
V. N. Denisov
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
The Cauchy Problem ◽  
Solution Gradient

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.

Very slow grow-up of solutions of a semi-linear parabolic equation

2011 ◽  
Vol 54 (2) ◽  
pp. 381-400 ◽  
Author(s):  
Marek Fila ◽  
John R. King ◽  
Michael Winkler ◽  
Eiji Yanagida
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Large Time ◽  
Global Solutions ◽  
Linear Parabolic Equation ◽  
Time Behaviour ◽  
Initial Value ◽  
The Cauchy Problem ◽  
Supercritical Nonlinearity ◽  
Singular Steady State

AbstractWe consider large-time behaviour of global solutions of the Cauchy problem for a parabolic equation with a supercritical nonlinearity. It is known that the solution is global and unbounded if the initial value is bounded by a singular steady state and decays slowly. In this paper we show that the grow-up of solutions can be arbitrarily slow if the initial value is chosen appropriately.

scholarly journals THE VALUE OF THE SOLUTION OF ONE PROBLEM FOR THE PSEUDOPARABOLIC EQUATION IN THE CLASS OF GELS

2020 ◽  
Vol 70 (2) ◽  
pp. 77-83
Author(s):  
U.K. Koylyshov ◽  
◽  
A.Zh. Aldashova ◽  
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Fundamental Solution ◽  
A Priori Estimates ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Initial Condition ◽  
Pseudoparabolic Equation ◽  
Volume Potential ◽  
The Cauchy Problem

This article discusses the Cauchy problem for a pseudo-parabolic equation in three-dimensional space. The result can be generalized to - dimensional space. The Cauchy problem for equations of parabolic and elliptic types is well studied. For a pseudo-parabolic equation using the previously constructed fundamental solution, evaluating the fundamental solution and its derivatives. Applying the Fourier transform with respect to and the Laplace transform with, we first obtained a priori estimates for the potentials of the initial condition and the volume potential in Hölder spaces. Further, using these results, we have proved an estimate of the solution of the Cauchy problem for the pseudo-parabolic equation in Hölder classes. A detailed proof of the estimation of the potentials of the initial condition, the volume potential, and the solution of the Cauchy problem for the pseudoparabolic equation is given

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