Electron. J. Diff. Equ., Vol. 2011 (2011), No. 71, pp. 1-13.

Compact decoupling for thermoviscoelasticity in irregular domains

El Mustapha Ait Ben Hassi, Hammadi Bouslous, Lahcen Maniar

Abstract:
Our goal is to prove the compactness of the difference between the thermoviscoelasticity semigroup and its decoupled semigroup. To show this, we prove the norm continuity of this difference, the compactness of the difference of their resolvents and use Theorem 2.3 in Huang [4]. We generalize a result by Liu [5]. An illustrative example of a thermoviscoelastic system with Neumann Laplacian on a Jelly Roll domain is given.

Submitted August 24, 2010. Published May 31, 2011.
Math Subject Classifications: 34G10, 47D06.
Key Words: Thermoviscoelasticity; semigroup compactness; semigroup norm continuity, essential spectrum; fractional power.

Show me the PDF file (217 KB), TEX file, and other files for this article.

El Mustapha Ait Ben Hassi
Département de Mathématiques
Faculté des Sciences Semlalia,
Université Cadi Ayyad, Marrakech 40000, B.P. 2390, Maroc
email: m.benhassi@ucam.ac.ma
Hammadi Bouslous
Département de Mathématiques
Faculté des Sciences Semlalia,
Université Cadi Ayyad, Marrakech 40000, B.P. 2390, Maroc
email: bouslous@ucam.ac.ma
Lahcen Maniar
Département de Mathématiques
Faculté des Sciences Semlalia,
Université Cadi Ayyad, Marrakech 40000, B.P. 2390, Maroc
email: maniar@ucam.ac.ma

Return to the EJDE web page