WELL-POSEDNESS AND DIRECT INTERNAL STABILITY OF COUPLED NON-DEGENRATE KIRCHHOFF SYSTEM VIA HEAT CONDUCTION

AKRAM BEN AISSA

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WELL-POSEDNESS AND DIRECT INTERNAL STABILITY OF COUPLED NON-DEGENRATE KIRCHHOFF SYSTEM VIA HEAT CONDUCTION

机译：WELL-POSEDNESS AND DIRECT INTERNAL STABILITY OF COUPLED NON-DEGENRATE KIRCHHOFF SYSTEM VIA HEAT CONDUCTION

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In the paper under study, we consider the following coupled non-degenerate Kirchhoff system {y_(tt)-φ(∫_Ω｜▽y｜~2dx)△y+α△θ=0, in Ω×(0,+∞) θ_t-△θ-β△yt=0, in Ω×(0,+∞) y = θ = 0, on (б)Ω×(0,+∞) y(?; 0) = y0; yt(?; 0) = y1; θ(?; 0) = θ_0; in Ω where Ω is a bounded open subset of R~n, α and β be two nonzero real numberswith the same sign and φ is given by φ(s) = m0 + m1s with some positiveconstants m0 and m1. So we prove existence of solution and establish itsexponential decay. The method used is based on multiplier technique andsome integral inequalities due to Haraux and Komornik5, 8.

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《Discrete and continuous dynamical systems, Series S》 |2022年第5期|983-993|共11页
作者
AKRAM BEN AISSA;
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作者单位

UR Analysis and Control of PDE's, UR 13ES64Higher Institute of transport and Logistics of SousseUniversity of Sousse, Tunisia;

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Well-posedness; exponential decay; multiplier method; internal stability; non-degenrate Kirchhoff system; heat conduction;

WELL-POSEDNESS AND DIRECT INTERNAL STABILITY OF COUPLED NON-DEGENRATE KIRCHHOFF SYSTEM VIA HEAT CONDUCTION

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