scholarly journals Asymptotic behavior of singular solutions for a semilinear parabolic equation

2012 ◽  
Vol 32 (11) ◽  
pp. 4027-4043 ◽  
Author(s):  
Shota Sato ◽  
Eiji Yanagida
Keyword(s):  
Asymptotic Behavior ◽  
Parabolic Equation ◽  
Singular Solutions ◽  
Semilinear Parabolic Equation ◽  
Semilinear Parabolic

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.

scholarly journals Measure Control of a Semilinear Parabolic Equation with a Nonlocal Time Delay

2018 ◽  
Vol 56 (6) ◽  
pp. 4434-4460
Author(s):  
Eduardo Casas ◽  
Mariano Mateos ◽  
Fredi Tröltzsch
Keyword(s):  
Parabolic Equation ◽  
Time Delay ◽  
Semilinear Parabolic Equation ◽  
Semilinear Parabolic
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