Asymptotic behavior of a semilinear problem in heat conduction with memory

Nonlinear Differential Equations and Applications

Volumn 5, Issue 3, 1998, Pages 333-354

  Giorgi, Claudio ^a   Pata, Vittorino ^a   Marzocchi, Alfredo ^b  

^a UNIVERSITY OF BRESCIA   (Italy)

^b UNIVERSITÀ CATTOLICA DEL SACRO CUORE   (Italy)

Author keywords

Absorbing set; Asymptotic behavior; Existence and uniqueness; Heat equation; Integro partial differential equations

Indexed keywords

EID: 0002693827     PISSN: 10219722     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000300050049     Document Type: Article

References (27)

1. S. AIZICOVICI, V. BARBU - Existence and asymptotic results for a system of integro-partial differential equations, NoDEA 3, 1-18, 1996.
2. V. BARBU - A semigroup approach to an infinite delay equation in Hilbert space, Abstract Cauchy problems and functional differential equations, F. Kappel and W. Schappacher, eds., Research Notes in Math. 48, 1-25, Pitman, Boston, 1981.
3. V. BARBU, M.A. MALIK - Semilinear integro-differential equations in Hilbert space, J. Math. Anal. Appl. 67, 452-475, 1979.
4. G. BONFANTI, P. COLLI, M. GRASSELLI, F. LUTEROTTI - Nonsmooth kernels in a phase relaxation problem with memory, Nonlinear Anal. 32, 455-465, 1998.
5. B.D. COLEMAN, M.E. GURTIN - Equipresence and constitutive equations for rigid heat conductors, Z. Angew. Math. Phys. 18, 199-208, 1967.
6. P. COLLI, M. GRASSELLI - Phase transition problems in materials with memory, J. Integral Equations Appl. 5, 1-22, 1993.
7. M.G. CRANDALL, S.O. LONDEN, J.A. NOHEL - An abstract nonlinear Volterra integrodifferential equation, J. Math. Anal. Appl. 64, 701-735, 1978.
8. C.M. DAFERMOS - Asymptotic stability in viscoelasticity, Arch. Rational Mech. Anal. 37, 297-308, 1970.
9. C.M. DAFERMOS, M. SLEMROD - Asymptotic behaviour of nonlinear contraction semigroups, J. Funct. Anal. 13, 97-106, 1973.
10. W. DESCH, R.K. MILLER - Exponential stabilization of Volterra integrodifferential equations in Hilbert spaces, J. Differential Equations 70, 366-389, 1987.
11. G. GENTILI - Dissipativity conditions and variational principles for the heat flux equation with linear memory, Diff. Int. Equat. 4, 977-989, 1991.
12. G. GENTILI, C. GIORGI - Thermodynamic properties and stability for the heat flux equation with linear memory, Quart. Appl. Math. 51, 342-362, 1993.
13. J.M. GHIDAGLIA, A. MARZOCCHI - Longtime behavior of strongly damped wave equations, global attractors and their dimension, SIAM J. Math. Anal. 22, 879-895, 1991.
14. H. GRABMÜLLER - On linear theory of heat conduction in materials with memory, Proc. Roy. Soc. Edinburgh A-76, 119-137, 1976-77.
15. M. GRASSELLI, V. PATA - Long time behavior of a homogenized model in viscoelastodynamics, Discrete Contin. Dynam. Systems 4, 339-358, 1998.
16. J.L. LIONS - Quelques méthodes de résolutions des problèmes aux limites non linéaires, Dunod Gauthier-Villars, Paris, 1969.
17. S.O. LONDEN, J.A. NOHEL - Nonlinear Volterra integrodifferential equation occurring in heat flow, J. Integral Equations 6, 11-50, 1984.
18. Y.I. LYSIKOV - On the possibility of development of vibrations during heating of the transparent dielectric by optical radiation, Zh. Prikl. Math, i Tekh. Fiz. 4, 56-59, 1984.
19. R.K. MILLER - An integrodifferential equation for rigid heat conductors with memory, J. Math. Anal. Appl. 66, 331-332, 1978.
20. J.W. NUNZIATO - On heat conduction in materials with memory, Quart. Appl. Math. 29, 187-204, 1971.
21. A. PAZY - Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York, 1983.
22. H. PETZELTOVÁ -Solution semigroup and invariant manifolds for functional equations with infinite delay, Math. Bohemica 118, 175-193, 1993.
23. M. SLEMROD - A hereditary partial differential equation with applications in the theory of simple fluids, Arch. Rational Mech. Anal. 62, 303-321, 1976.
24. M. SLEMROD - An energy stability method for simple fluids, Arch. Rational Mech. Anal. 68, 1-18, 1978.
25. O. STAFFANS - Semigroups generated by a convolution equation, Infinite dimensional systems, F. Kappel and W. Schappacher, eds., Lecture Notes in Math. 1076, Springer-Verlag, Berlin, 1984.
26. R. TEMAM - Navier Stokes equations, theory and numerical analysis, North-Holland, Amsterdam, 1979.
27. R. TEMAM - Infinite-dimensional dynamical systems in mechanics and physics, Springer-Verlag, New York, 1988.