Life span of solutions with large initial data in a semilinear parabolic equation

2001 ◽  
Vol 50 (1) ◽  
pp. 591-610 ◽  
Author(s):  
Eiji Yanagida ◽  
Noriko Mizoguchi
Keyword(s):  
Parabolic Equation ◽  
Initial Data ◽  
Life Span ◽  
Semilinear Parabolic Equation ◽  
Large Initial Data ◽  
Semilinear Parabolic

scholarly journals Error Estimates for Solutions of the Semilinear Parabolic Equation in Whole Space

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Xiaomei Hu
Keyword(s):  
Parabolic Equation ◽  
Initial Data ◽  
Error Estimates ◽  
Three Dimensional ◽  
Semilinear Parabolic Equation ◽  
Energy Methods ◽  
Analysis Technique ◽  
Whole Space ◽  
Fourier Analysis Technique ◽  
Semilinear Parabolic

This paper is focused on the error estimates for solutions of the three-dimensional semilinear parabolic equation with initial datau0∈L2(ℝ3). Employing the energy methods and Fourier analysis technique, it is proved that the error between the solution of the semilinear parabolic equation and that of linear heat equation has the behavior asO((1+t)−3/8).

scholarly journals Life span of solutions with large initial data for a semilinear parabolic system coupling exponential reaction terms

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Sen Zhou
Keyword(s):  
Lower Bound ◽  
Initial Data ◽  
Life Span ◽  
Parabolic Equations ◽  
Coupled Systems ◽  
Large Initial Data ◽  
Semilinear Parabolic System ◽  
Systems Of Parabolic Equations ◽  
System Coupling ◽  
Semilinear Parabolic

Abstract In this paper, we study a coupled systems of parabolic equations subject to large initial data. By using comparison principle and Kaplan’s method, we get the upper and lower bound for the life span of the solutions.

Asymptotically self-similar global solutions of a semilinear parabolic equation with a nonlinear gradient term

1999 ◽  
Vol 129 (6) ◽  
pp. 1291-1307 ◽  
Author(s):  
S. Snoussi ◽  
S. Tayachi ◽  
F. B. Weissler
Keyword(s):  
Parabolic Equation ◽  
Initial Data ◽  
Asymptotic Behaviour ◽  
Global Solutions ◽  
Gradient Term ◽  
Semilinear Parabolic Equation ◽  
Small Initial Data ◽  
Self Similar ◽  
Semilinear Parabolic

We study the existence and the asymptotic behaviour of global solutions of the semilinear parabolic equation u(0) = ϧwhere a, b ∈ℝ, q > 1, p > 1. Forq=2p/(p+1) and ½ 1(p-1)>1 (equivalently, q > (n + 2)/(n + 1)), we prove the existence of mild global solutions for small initial data with respect to some norm. Some of those solutions are asymptotically self-similar.

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