References
- Deseri , L , Fabrizio , M and Golden , JM . 2006 . On the concept of a minimal state in viscoelasticity: New free energies and applications to PDE S . Arch. Rational Mech. Anal. , 181 ( 1 ) : 43 – 96 .
- Fabrizio , M and Golden , JM . 2002 . Maximum and minimum free energies for a linear viscoelastic material . Quart. Appl. Math. , LX ( 2 ) : 341 – 381 .
- Joseph , DD . 1990 . Fluid Dynamics of Viscoelastic Liquids , New York : Springer Verlag .
- Truesdell , C . 1974 . The meaning of viscometry in fluid dynamics . Ann. Rev. Fluid Mech. , 6 : 111 – 146 .
- Fabrizio , M and Lazzari , B . 1991 . On the existence and the asymptotic stability of solutions for linearly viscoelastic solids . Arch. Rational Mech. Anal. , 116 ( 2 ) : 139 – 152 .
- Sneddon , IN . 1972 . The Use of Integral Transforms , New York : McGraw-Hill .
- Amendola , G and Fabrizio , M . 2007 . Maximum recoverable work for incompressible viscoelastic fluids and application to a discrete spectrum model . Diff. Int. Equ. , 20 ( 4 ) : 445 – 466 .
- Fabrizio , M and Lazzari , B . 1993 . On asymptotic stability for linear viscoelastic fluids . Diff. Int. Equ. , 6 ( 3 ) : 491 – 504 .
- Fabrizio , M and Morro , A . 1992 . Mathematical Problems in Linear Viscoelasticity , Philadelphia : SIAM .
- Graffi , D . 1982 . Sull'espressione analitica di alcune grandezze termodinamiche nei materiali con memoria . Rend. Sem. Mat. Univ. Padova , 68 : 17 – 29 .
- Graffi , D . 1986 . Ancora sull'espressione dell'energia libera nei materiali con memoria . Atti Acc. Sci. Torino , 120 : 111 – 124 .
- Volterra , V . 1930 . Theory of Functional and of Integral and Integro-differential Equations , London : Blackie & Son Limited .
- Slemrod , M . 1978 . An energy stability method for simple fluids . Arch. Rational Mech. Anal. , 68 : 1 – 18 .
- Amendola , G , Fabrizio , M and Golden , JM . Maximum recoverable work and free energies for incompressible viscoelastic fluids . Ukrainian Math. J. , to appear
- Golden , JM . 2000 . Free energies in the frequency domain: The scalar case . Quart. Appl. Math. , 58 : 127 – 150 .
- Amendola , G . 2006 . The minimum free energy for incompressible viscoelastic fluids . Math. Meth. Appl. Sci. , 29 : 2201 – 2223 .
- Muskhelishvili , NI . 1953 . Singular Integral Equations. Boundary Problems of Function Theory and their Application to Mathematical Physics , Groningen : Noordhoff .
- Dafermos , CM . 1970 . Asymptotic stability in viscoelasticity . Arch. Rational Mech. Anal. , 37 : 297 – 308 .
- Pazy , A . 1974 . Semigroups of Linear Operators and Applications to Partial Differential Equations Lectures Notes in Mathematics, 10 , Maryland : University of Maryland .
- Datko , R . 1970 . Extending a theorem of A.M. Liapunov to Hilbert spaces . J. Math. Anal. Appl. , 32 : 610 – 616 .