Stability for a nonlinear coupled system of elasticity and thermoelasticity with second sound
2014 ◽
Vol 13
(01)
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pp. 45-75
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Keyword(s):
In this paper, we study the qualitative properties of solutions to a nonlinear system describing the motion of a bar in which the middle part is sensitive to the thermal change, while the outer parts are insensible. By the energy method, we show that the initial boundary value problem for this coupled system of wave equations and thermoelastic equations with second sound in one space variable is well-posed globally in time, and it is also stable exponentially as the time goes to infinity when the wave speed of the outer parts is properly large, under certain restrictions on the initial data and the growth rate of the nonlinear terms.
1990 ◽
Vol 146
(1)
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pp. 217-240
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2007 ◽
Vol 2007
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pp. 1-9
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2013 ◽
Vol 403
(1)
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pp. 89-94
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2014 ◽
Vol 2014
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pp. 1-9
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2003 ◽
Vol 55
(3)
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pp. 765-795
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2011 ◽
Vol 141
(4)
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pp. 865-880
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