2012, 2(1): 91-104. doi: 10.3934/naco.2012.2.91

Solvability of a class of thermal dynamical contact problems with subdifferential conditions

1. 

Institut d'Ingénierie Informatique de Limoges and LACO, URA-1586, 123 Avenue A. Thomas, 87060 Limoges Cedex

2. 

Université de La Réunion, Département Maths-Info, BP 7151, 15 Avenue René Cassin, 97715 Saint Denis Messag, cedex 09, La Réunion

Received  January 2011 Revised  August 2011 Published  March 2012

We study a class of dynamic thermal sub-differential contact problems with friction, for long memory visco-elastic materials, which can be put into a general model of system defined by a second order evolution inequality, coupled with a first order evolution equation. We present and establish an existence and uniqueness result, by using general results on first order evolution inequality, with monotone operators and fixed point methods.
Citation: Samir Adly, Oanh Chau, Mohamed Rochdi. Solvability of a class of thermal dynamical contact problems with subdifferential conditions. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 91-104. doi: 10.3934/naco.2012.2.91
References:
[1]

Applicable Analysis, 83 (2004), 635-648. doi: 10.1080/00036810410001657233.  Google Scholar

[2]

Editura Academiei, Bucharest-Noordhoff, Leyden, 1976. Google Scholar

[3]

J. Math. Pures et Appli., 51 (1972), 1-168. Google Scholar

[4]

Int. J. of Appli. Math. and Mech., 2 (2006), 41-52. Google Scholar

[5]

North-Holland, 1988.  Google Scholar

[6]

C.R. Acad. Sci. Paris, Ser. I, 338 (2004), 341-346.  Google Scholar

[7]

Dunod, Paris, 1972.  Google Scholar

[8]

Chapman and Hall, 2005. doi: 10.1201/9781420027365.  Google Scholar

[9]

Kluwer Academic Publishers, 2003.  Google Scholar

[10]

Mathematical Models and Methods in Applied Sciences, 9 (1999), 11-34. doi: 10.1142/S0218202599000038.  Google Scholar

[11]

SIAM, Philadelphia, 1988. doi: 10.1137/1.9781611970845.  Google Scholar

[12]

Dunod et Gauthier-Villars, 1969. Google Scholar

[13]

Bolletino U.M.I., 17 (1980), 796-811.  Google Scholar

[14]

Elsevier, Amsterdam, 1981. Google Scholar

[15]

Birkhäuser, Basel, 1985. doi: 10.1007/978-1-4612-5152-1.  Google Scholar

[16]

Springer-Verlag, 1993.  Google Scholar

[17]

Springer Verlag, 1997. Google Scholar

show all references

References:
[1]

Applicable Analysis, 83 (2004), 635-648. doi: 10.1080/00036810410001657233.  Google Scholar

[2]

Editura Academiei, Bucharest-Noordhoff, Leyden, 1976. Google Scholar

[3]

J. Math. Pures et Appli., 51 (1972), 1-168. Google Scholar

[4]

Int. J. of Appli. Math. and Mech., 2 (2006), 41-52. Google Scholar

[5]

North-Holland, 1988.  Google Scholar

[6]

C.R. Acad. Sci. Paris, Ser. I, 338 (2004), 341-346.  Google Scholar

[7]

Dunod, Paris, 1972.  Google Scholar

[8]

Chapman and Hall, 2005. doi: 10.1201/9781420027365.  Google Scholar

[9]

Kluwer Academic Publishers, 2003.  Google Scholar

[10]

Mathematical Models and Methods in Applied Sciences, 9 (1999), 11-34. doi: 10.1142/S0218202599000038.  Google Scholar

[11]

SIAM, Philadelphia, 1988. doi: 10.1137/1.9781611970845.  Google Scholar

[12]

Dunod et Gauthier-Villars, 1969. Google Scholar

[13]

Bolletino U.M.I., 17 (1980), 796-811.  Google Scholar

[14]

Elsevier, Amsterdam, 1981. Google Scholar

[15]

Birkhäuser, Basel, 1985. doi: 10.1007/978-1-4612-5152-1.  Google Scholar

[16]

Springer-Verlag, 1993.  Google Scholar

[17]

Springer Verlag, 1997. Google Scholar

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