GLOBAL EXISTENCE OF SOLUTIONS FOR A WEAKLY COUPLED SYSTEM OF THREE DAMPED [sigma]-EVOLUTION EQUATIONS

In this paper our purpose is the study of the Cauchy problem for weakly coupled system of three semi-linear damped [sigma]-evolution equations. Using ([L.sup.m] [intersection] [L.sup.2]) - [L.sup.2] linear estimates combined with fractional Gagliardo-Nirenberg inequality. We find the so-called ([p.s...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 14; no. 3; p. 873
Main Author Djaouti, A. Mohammed
Format Journal Article
LanguageEnglish
Published Turkic World Mathematical Society 01.07.2024
Subjects
Analysis
Cauchy problem
Damping (Mechanics)
Existence theorems
Saudi Arabia
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Summary:In this paper our purpose is the study of the Cauchy problem for weakly coupled system of three semi-linear damped [sigma]-evolution equations. Using ([L.sup.m] [intersection] [L.sup.2]) - [L.sup.2] linear estimates combined with fractional Gagliardo-Nirenberg inequality. We find the so-called ([p.sub.1] - [p.sub.2] - [p.sub.3]) planes for the global (in time) existence. Moreover, from the interaction between the parameters [m.sub.1], [m.sub.2], [m.sub.3] [member of] [1, 2) in one hand and [[sigma].sub.1], [[sigma].sub.2], [[sigma].sub.3] [greater than or equal to] 1 in the other hand. We proved lower bounds for powers nonlinearities similarly to the modified Fujita exponent, which are in the form of planes ([p.sub.1] - [p.sub.2]), ([p.sub.1] - [p.sub.3]) and ([p.sub.2] - [p.sub.3]). Weakly coupled system; [sigma]-evolution equation; frictional damping, visco-elastic damping, Additional regularity; Global existence. AMS Subject Classification: 35L52, 35B44.
ISSN:2146-1147