Set-Valued Pseudomonotone Maps and Degenerate Evolution Inclusions

Kuttler, Kenneth; Shillor, Meir

doi:10.1142/s0219199799000067

Cited by 71 publications

(44 citation statements)

References 12 publications

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“…The assumptions on the functions used in modeling the contact are weak enough to include both the normal compliance and the Tresca model. A similar result was obtained recently by Kuttler and Schillor [11]. There, an abstract existence and uniqueness theorem has been used.…”

Section: Introductionsupporting

confidence: 55%

“…A similar theorem was obtained recently by Kuttler and Schillor [11]. There, an abstract existence and uniqueness theorem has been used.…”

Section: Il(t)v -U(t)) + A(u(t) V -U(t)) + R]c(u(t)v -U(t))mentioning

confidence: 75%

“…Concerning the uniqueness result, in [11] is considered the particular case of a bounded tangential stress, i.e., hx is supposed to be a bounded function.…”

Section: Il(t)v -U(t)) + A(u(t) V -U(t)) + R]c(u(t)v -U(t))mentioning

confidence: 99%

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Viscosity solutions for dynamic problems with slip-rate dependent friction

Ionescu¹

2002

Quart. Appl. Math.

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Abstract.The dynamic evolution of an elastic medium undergoing frictional slip is considered. The Coulomb law modeling the contact uses a friction coefficient that is a non-monotone function of the slip-rate. This problem is ill-posed, the solution is nonunique and shocks may be created on the contact interface. In the particular case of the one-dimensional shearing of an elastic slab, the (perfect) delay convention can be used to select a unique solution. Different solutions in acceleration and deceleration processes are obtained. To transform the ill-posed problem into a well-posed one and to justify the choice of the perfect delay criterion, a visco-elastic constitutive law with a small viscosity is used here. An existence and uniqueness result is obtained in three dimensions. The assumptions on the functions implied in the contact model are weak enough to include both the normal compliance and the Tresca model. The following conjecture, based on results of numerical simulations, is stated: in the elastic case, the solution chosen by the perfect delay convention is the one obtained from the solutions of the problem with viscosity, when the viscosity tends to zero.

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Section: Introductionsupporting

confidence: 55%

“…A similar theorem was obtained recently by Kuttler and Schillor [11]. There, an abstract existence and uniqueness theorem has been used.…”

Section: Il(t)v -U(t)) + A(u(t) V -U(t)) + R]c(u(t)v -U(t))mentioning

confidence: 75%

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Viscosity solutions for dynamic problems with slip-rate dependent friction

Ionescu¹

2002

Quart. Appl. Math.

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“…The solutions of these problems are obtained by using a version of an abstract existence theorem for degenerate first-order evolution equations obtained by Kuttler in [14] (see also [16] for a generalization of the theorem) which we now recall.…”

Section: Quasistatic Frictional Bilateral Contact Problem 547mentioning

confidence: 99%

“…3 where we use an abstract existence result for degenerate evolution equations due to [14]. We note in passing that a considerable generalization of this theorem can be found in [16]. Then we obtain the necessary a priori estimates on the solutions.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness for a quasistatic frictional bilateral contact problem in thermoviscoelasticity

Rochdi¹,

Shillor²

2000

Quart. Appl. Math.

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Abstract.We prove the existence and uniqueness of the weak solution for a quasistatic thermoviscoelastic problem which describes bilateral frictional contact between a deformable body and a moving rigid foundation. The model consists of the heat equation for the temperature, the elliptic viscoelasticity system for the displacements, the SJK-Coulomb law of friction and frictional heat generation condition. The proof is accomplished in two steps. First, the existence of solutions for a regularized problem is established and a priori estimates obtained. Then the limit function, which is the weak solution of the original problem, is shown to be the unique fixed point of the solution operator when the friction coefficient is small.

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