scholarly journals Life span of solutions with large initial data for a semilinear parabolic system

2011 ◽  
Vol 380 (2) ◽  
pp. 632-641 ◽  
Author(s):  
Shota Sato
Keyword(s):  
Initial Data ◽  
Life Span ◽  
Parabolic System ◽  
Large Initial Data ◽  
Semilinear Parabolic System ◽  
Semilinear Parabolic

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.

ASYMPTOTIC SELF-SIMILAR BEHAVIOR OF SOLUTIONS FOR A SEMILINEAR PARABOLIC SYSTEM

2001 ◽  
Vol 03 (03) ◽  
pp. 363-392 ◽  
Author(s):  
SEIFEDDINE SNOUSSI ◽  
SLIM TAYACHI
Keyword(s):  
Initial Data ◽  
Parabolic System ◽  
Large Time ◽  
Space Dimension ◽  
Mild Solutions ◽  
Small Initial Data ◽  
Semilinear Parabolic System ◽  
Self Similar ◽  
Similar Solutions ◽  
Semilinear Parabolic

This paper studies the global existence and the asymptotic self-similar behavior of solutions of the semilinear parabolic system ∂tu=Δu+a1|u|p1-1u+b1|v|q1-1v, ∂tv=Δv+a2|v|p2-1v+b2|u|q2-1u, on (0,∞)×ℝn, where a1, bi∈ℝ and pi, qi>1. Let p= min {p1,p2, q1(1+q2)/(1+q1), q2(1+q1)/(1+q2)}. Under the condition p>1+2/n we prove the existence of globally decaying mild solutions with small initial data. Some of them are asymptotic, for large time, to self-similar solutions of appropriate asymptotic systems having each one a self-similar structure. All possible asymptotic self-similar behaviors are discussed in terms of exponents pi, qi, the space dimension n and the asymptotic spatial profile of the related initial data.

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