Thermoelastic contact with Barber's heat exchange condition

Andrews, Kevin T.; Shi, Peter; Shillor, Meir; Wright, Steve

doi:10.1007/bf01188756

Cited by 56 publications

(27 citation statements)

References 26 publications

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“…where , , ␣ , ␣ are given positive constants. 1.9 says that the heat 1 2 1 2 flux in both rods is proportional to the temperature difference of the free edges. It should be pointed out here that if we take ␣ s ␣ s 1, then the 1 2 Ž .…”

Section: Xmentioning

confidence: 98%

The Thermoelastic and Viscoelastic Contact of Two Rods

Rivera¹,

Jiang

1998

Journal of Mathematical Analysis and Applications

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We consider the thermoelastic and viscoelastic contact problem of two rods and prove the existence of a weak solution using a penalization method and compensated compactness. Moreover, for the thermoelastic contact we show that the weak solution converges to zero exponentially as time goes to infinity, and for the viscoelastic contact we prove that the weak solution decays to zero with the same rates as the relaxation functions do. ᮊ

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Section: Xmentioning

confidence: 98%

The Thermoelastic and Viscoelastic Contact of Two Rods

Rivera¹,

Jiang

1998

Journal of Mathematical Analysis and Applications

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“…Andrew et al [5] obtained the existence and uniqueness of problem (1.1)-(1.6) and (1.8) under the restriction that a Ͻ 1. Copetti [1] gave the existence and uniqueness of a strong solution to (1.1)-(1.7) and used his results to drop the restriction a Ͻ 1 in Signorini's problem.…”

Section: )mentioning

confidence: 98%

Numerical solution to a one-dimensional thermoplastic problem with unilateral constraint

Zhao

Sun

Liu

2006

Numer. Methods Partial Differential Eq.

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In this article, we present a numerical simulation of one-dimensional problem of quasi-static contact with an elastic obstacle. A finite difference scheme is derived by the method of reduction of order on uniform meshes. The stability and convergence are proved. The convergence order is of O( 2 ϩ h 2 ), where and h are the time step size and the space step size, respectively. Some numerical examples demonstrate the theoretical results.

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“…We refer to Carlson ([3]) and Day ([6]) for physical background and mathematical modelling. Existence results to this problem were obtained by Andrews et al in [1] using a heat transfer coefficient which may depend on the contact pressure and the distance of the right edge from the obstacle. Some numerical experiments using a finite difference scheme were performed by Shi et al in [11].…”

Section: )(U(1 T) − G) =mentioning

confidence: 99%