Asymptotic property of singular solutions in some nonstandard parabolic equation

2021 ◽  
Vol 60 ◽  
pp. 103301
Author(s):  
Yuxi Wang ◽  
Bingchen Liu ◽  
Yurou Sun
Keyword(s):  
Parabolic Equation ◽  
Asymptotic Property ◽  
Singular Solutions

scholarly journals Very singular solutions to a nonlinear parabolic equation with absorption II. Uniqueness

2004 ◽  
Vol 134 (1) ◽  
pp. 39-54 ◽  
Author(s):  
Saïd Benachour ◽  
Herbert Koch ◽  
Philippe Laurençot
Keyword(s):  
Parabolic Equation ◽  
Nonlinear Parabolic Equation ◽  
Singular Solution ◽  
Singular Solutions ◽  
Nonlinear Parabolic ◽  
Self Similar ◽  
Image Position ◽  
Similar Solutions ◽  
Very Singular Solution

We prove the uniqueness of the very singular solution to when 1 < p < (N + 2)/(N + 1), thus completing the previous result by Qi and Wang, restricted to self-similar solutions.

Time-dependent singularities in a semilinear parabolic equation with absorption

2016 ◽  
Vol 18 (05) ◽  
pp. 1550077 ◽  
Author(s):  
Jin Takahashi ◽  
Eiji Yanagida
Keyword(s):  
Parabolic Equation ◽  
Singular Point ◽  
Fundamental Solution ◽  
Laplace Equation ◽  
Space Variable ◽  
The Other ◽  
Time Dependent ◽  
Singular Solutions ◽  
Semilinear Parabolic Equation ◽  
Semilinear Parabolic

This paper concerns solutions with time-dependent singularities for a semilinear parabolic equation with a superlinear absorption term. Here, by time-dependent singularity, we mean a singularity with respect to the space variable whose position depends on time. It is shown that if the power of the nonlinearity is in some range, then any singularity is removable. On the other hand, in other range, two types of time-dependent singular solutions exist: One resembles the fundamental solution of the Laplace equation near the singular point, and the other has a stronger singularity.

Very singular solutions to a nonlinear parabolic equation with absorption. I. Existence

2001 ◽  
Vol 131 (1) ◽  
pp. 27-44 ◽  
Author(s):  
Said Benachour ◽  
Philippe Laurençot
Keyword(s):  
Parabolic Equation ◽  
Nonlinear Parabolic Equation ◽  
Singular Solution ◽  
Singular Solutions ◽  
Nonlinear Parabolic ◽  
Image Position ◽  
Very Singular Solution

We prove the existence of a very singular solution to when 1 < p < (N + 2)/(N + 1).

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

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