Nonexistence of Global Positive Solutions of Weakly Coupled Systems of Semilinear Parabolic Equations with Time-Periodic Coefficients

2020 ◽  
Vol 56 (6) ◽  
pp. 721-733
Author(s):  
Sh. G. Bagyrov
Keyword(s):  
Positive Solutions ◽  
Parabolic Equations ◽  
Coupled Systems ◽  
Semilinear Parabolic Equations ◽  
Periodic Coefficients ◽  
Weakly Coupled ◽  
Weakly Coupled Systems ◽  
Semilinear Parabolic ◽  
Time Periodic

scholarly journals Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdelhamid Mohammed Djaouti
Keyword(s):  
Global Existence ◽  
Parabolic Equations ◽  
Coupled Systems ◽  
Time Dependent ◽  
Small Data ◽  
Weakly Coupled ◽  
Weakly Coupled Systems

AbstractWe prove the global existence of small data solution in all spaces of all dimensions $n\geq 1$ n ≥ 1 for weakly coupled systems of semilinear effectively damped wave, with different time-dependent coefficients in the dissipation terms. Moreover, we assume that the nonlinearity terms $f(t,u) $ f ( t , u ) and $g(t,v) $ g ( t , v ) satisfy some properties of parabolic equations. We study the problem in several classes of regularity.

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