scholarly journals SOME BLOW-UP PROPERTIES OF A SEMILINEAR HEAT EQUATION

2019 ◽  
pp. 31-33
Author(s):  
Maan A. Rasheed
Keyword(s):  
Heat Equation ◽  
Exponential Type ◽  
Nonlinear Term ◽  
Blow Up ◽  
Single Point ◽  
Rate Estimate ◽  
Semilinear Heat Equation ◽  
Blow Up Rate

In this paper, we consider some blow-up properties of a semilinear heat equation, where the nonlinear term is of exponential type, subject to the zero Dirichletboundary conditions, defined in a ball in 𝑅 𝑛 . Firstly, we study the blow-up set showing that the blow-up can only occur at a single point. Secondly, the upper blow-up rate estimate is derived.

scholarly journals Deriving The Upper Blow-up Rate Estimate for a Parabolic Problem

2020 ◽  
pp. 200-203
Author(s):  
Maan A. Rasheed
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Bounded Domain ◽  
Neumann Boundary Condition ◽  
Parabolic Problem ◽  
Blow Up ◽  
Neumann Boundary ◽  
Rate Estimate ◽  
Blow Up Rate

In this paper, the blow-up solutions for a parabolic problem, defined in a bounded domain, are studied. Namely, we consider the upper blow-up rate estimate for heat equation with a nonlinear Neumann boundary condition defined on a ball in Rn.

scholarly journals Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition

2019 ◽  
Vol 53 (1) ◽  
pp. 57-72
Author(s):  
Marcos Josías Ceballos-Lira ◽  
Aroldo Pérez
Keyword(s):  
Global Existence ◽  
Heat Equation ◽  
Mild Solution ◽  
Blow Up ◽  
Local Existence ◽  
Dirichlet Condition ◽  
Infinite Time ◽  
Diffusion Operator ◽  
Intrinsic Ultracontractivity ◽  
Semilinear Heat Equation

In this paper we prove the local existence of a nonnegative mild solution for a nonautonomous semilinear heat equation with Dirichlet condition, and give sucient conditions for the globality and for the blow up infinite time of the mild solution. Our approach for the global existence goes back to the Weissler's technique and for the nite time blow up we uses the intrinsic ultracontractivity property of the semigroup generated by the diffusion operator.

scholarly journals Stability of ODE blow-up for the energy critical semilinear heat equation

2017 ◽  
Vol 355 (1) ◽  
pp. 65-79 ◽  
Author(s):  
Charles Collot ◽  
Frank Merle ◽  
Pierre Raphaël
Keyword(s):  
Heat Equation ◽  
Blow Up ◽  
Semilinear Heat Equation

On backward self-similar blow-up solutions to a supercritical semilinear heat equation

2010 ◽  
Vol 140 (4) ◽  
pp. 821-831 ◽  
Author(s):  
Noriko Mizoguchi
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Blow Up ◽  
Radial Solution ◽  
Similar Solution ◽  
Semilinear Heat Equation ◽  
Blowing Up ◽  
Self Similar Solution ◽  
Self Similar ◽  
Image Position

We are concerned with a Cauchy problem for the semilinear heat equationthen u is called a backward self-similar solution blowing up at t = T. Let pS and pL be the Sobolev and the Lepin exponents, respectively. It was shown by Mizoguchi (J. Funct. Analysis257 (2009), 2911–2937) that k ≡ (p − 1)−1/(p−1) is a unique regular radial solution of (P) if p > pL. We prove that it remains valid for p = pL. We also show the uniqueness of singular radial solution of (P) for p > pS. These imply that the structure of radial backward self-similar blow-up solutions is quite simple for p ≥ pL.

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