### Abstract

We stablish an existence result for the thermoviscoelastic degenerated contact problem. The nonlinear stress-strain relation we will consider here is given by where M is a function satisfying M ∈ C^{1}(]0, ∞[) ∩ C([0, ∞[), M(s) ≥ C s ^{p}. Moreover, we show that the solution decays uniformly to zero. That is, denoting by E(t) the first-order energy associated to the equation, we show that there exist positive constants C satisfying E(t) ≤ C(E(0))(1 + t)^{-(p} ^{+} ^{2)/p} where p is a positive number which depends on nonlinear terms of the system.

Original language | English |
---|---|

Pages (from-to) | 522-545 |

Number of pages | 24 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 264 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2001 Dec 15 |

Externally published | Yes |

### Fingerprint

### Keywords

- Polynomial decay
- Signorini's problem
- Thermoviscoelasticity

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*264*(2), 522-545. https://doi.org/10.1006/jmaa.2001.7686

**The contact problem in thermoviscoelastic materials.** / Nakao, Mitsuhiro; Muñoz Rivera, Jaime E.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 264, no. 2, pp. 522-545. https://doi.org/10.1006/jmaa.2001.7686

}

TY - JOUR

T1 - The contact problem in thermoviscoelastic materials

AU - Nakao, Mitsuhiro

AU - Muñoz Rivera, Jaime E.

PY - 2001/12/15

Y1 - 2001/12/15

N2 - We stablish an existence result for the thermoviscoelastic degenerated contact problem. The nonlinear stress-strain relation we will consider here is given by where M is a function satisfying M ∈ C1(]0, ∞[) ∩ C([0, ∞[), M(s) ≥ C s p. Moreover, we show that the solution decays uniformly to zero. That is, denoting by E(t) the first-order energy associated to the equation, we show that there exist positive constants C satisfying E(t) ≤ C(E(0))(1 + t)-(p + 2)/p where p is a positive number which depends on nonlinear terms of the system.

AB - We stablish an existence result for the thermoviscoelastic degenerated contact problem. The nonlinear stress-strain relation we will consider here is given by where M is a function satisfying M ∈ C1(]0, ∞[) ∩ C([0, ∞[), M(s) ≥ C s p. Moreover, we show that the solution decays uniformly to zero. That is, denoting by E(t) the first-order energy associated to the equation, we show that there exist positive constants C satisfying E(t) ≤ C(E(0))(1 + t)-(p + 2)/p where p is a positive number which depends on nonlinear terms of the system.

KW - Polynomial decay

KW - Signorini's problem

KW - Thermoviscoelasticity

UR - http://www.scopus.com/inward/record.url?scp=0035894676&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035894676&partnerID=8YFLogxK

U2 - 10.1006/jmaa.2001.7686

DO - 10.1006/jmaa.2001.7686

M3 - Article

AN - SCOPUS:0035894676

VL - 264

SP - 522

EP - 545

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -