On the Uniqueness in Dynamical Thermoelasticity Backward in Time for Porous Media

REFERENCES

• J. Serrin , The Initial Value Problem for the Navier-Stokes Equations , Proceedings of the Symposium on Non-Linear Problems , University of Wisconsin Press , Madison , WI , pp. 69 – 98 , 1963 .
   Google Scholar
• R. J. Knops and L. E. Payne , On the Stability of Solutions of the Navier-Stokes Equations Backward in Time . Arch. Rational. Mech. Anal. vol. 29 , pp. 331 – 335 , 1968 .
   Web of Science ®Google Scholar
• G. P. Galdi and B. Straughan , Stability of Solutions of the Navier-Stokes Equations Backward in Time . Arch. Rational. Mech. Anal. vol. 101 , pp. 107 – 114 , 1988 .
   Web of Science ®Google Scholar
• L. E. Payne , and B. Straughan , Improperly Posed, and Non-standard Problems for Parabolic Partial Differential Equations , G. Eason , and Row. Ogden (eds.) Elasticity: Mathematical Methods and Applications, The Ian N. Sneddon 70th Birthday Volume , Ellis Horwood , Chichester , UK , pp. 273 – 299 , 1990 .
   Google Scholar
• K. A. Ames and L. E. Payne , Stabilizing Solutions of the Equations of Dynamical Thermoelasticity Backward in Time , Stab. Appl. Anal. Contin. Media vol. 1 , pp. 243 – 260 , 1991 .
   Google Scholar
• M. Ciarletta , and S. Chirita , Spatial Behavior in Dynamical Thermoelasticity Backward in Time , Fourth International Congress on Thermal Stresses , Osaka , Japan , pp. 485 – 488 , 2001 .
   Google Scholar
• M. Ciarletta , and S. Chirita , Asymptotic Partition in the Linear Thermoelasticity Backward in Time , Mathematical Models and Methods for Smart Materials , World Scientific, 62 , pp. 31 – 41 , 2002 .
   Google Scholar
• M. Ciarletta , On the Uniqueness and Continuous Dependence of Solutions in Dynamical Thermoelasticity Backward in Time , J. Therm. Stresses vol. 25 , pp. 969 – 984 , 2002 .
   Web of Science ®Google Scholar
• G. Iovane , and F. Passarella , Spatial Behavior in Dynamical Thermoelasticity Backward in Time for Porous Media . J. Thermal Stresses , vol. 27 , pp. 97 – 109 , 2004 .
   Web of Science ®Google Scholar
• F. Passarella and V. Tibullo , Some Results in Linear Theory of Thermoelasticity Backward in Time for Microstretch Materials . J. Therm. Stresses vol. 33 , pp. 559 – 576 , 2010 .
   Web of Science ®Google Scholar
• A. C. Eringen , Linear Theory of Micropolar Elasticity , Int. J. Math. Mech. , vol. 15 , pp. 909 – 923 , 1966 .
   Web of Science ®Google Scholar
• A. C. Eringen , Theory of Micropolar Elasticity , in H. Leibowitz (ed.), Fracture , vol. II , Academic Press , New York , p. 622 , 1968 .
   Google Scholar
• A. C. Eringen , Foundations of Micropolar Thermoelasticity, Courses and Lectures , no. 23, CISM Udine , Springer-Verlag , Vienna and New York , 1970 .
   Google Scholar
• A. C. Eringen , Microcontinuum Field Theories I: Foundations and Solids , Springer-Verlag , New York , Berlin , Heidelberg , 1999 .
   Google Scholar
• A. C. Eringen and C. B. Kafadar , Polar Field Theories , in A. C. Eringen (ed.), Continuum Physics , vol. IV , Part I, Academic Press , New York , 1976 .
   Google Scholar
• W. Nowacki , Theory of Asymmetric Elasticity , Polish Scientific Publishers/Pergamon Press , Warszawa, Oxford , New York , Paris, Frankfurt , 1986.
   Google Scholar
• M. Ciarletta , Sui Processi Termoelastici Per Continui Micropolari , Atti Sem. Mat. Fis. Univ. Modena , vol. 39 , pp. 103 – 111 , 1991 .
   Google Scholar
• M. Ciarletta and D. Iesan , Non-Classical Elastic Solids , in Pitman, Research Notes in Mathematics Series (Longman Scientific & Technical) , vol. 293 , 1993 .
   Google Scholar
• J. Dyszlewicz , Micropolar Theory of Elasticity , Lect. Notes Appl. Comput. Mech. , vol. 15 , Springer , Berlin , Heidelberg, New York , 2004 .
   Google Scholar
• D. Iesan , Thermoelastic Models of Continua , Kluwer Academic Publishers , Dordrecht , 2004 .
   Google Scholar
• M. Ciarletta , B. Straughan , and V. Tibullo , Structural Stability for a Rigid Body with Thermal Microstructure , Int. J. Eng. Sci. , vol. 48 , no. 6 , pp. 592 – 598 , 2010 .
   Google Scholar
• F. Passarella , Some Results in Micropolar Thermoelasticity , Mech. Res. Commun. , vol. 23 , no. 4 , pp. 349 – 357 , 1996 .
   Web of Science ®Google Scholar
• M. Svanadze , V. Tibullo , and V. Zampoli , Fundamental Solution in the Theory of Micropolar Thermoelasticity without Energy Dissipation , J. Therm. Stresses , vol. 29 , no. 1 , pp. 57 – 66 , 2006 .
   Web of Science ®Google Scholar
• F. Passarella and V. Zampoli , On the Theory of Micropolar Thermoelasticity without Energy Dissipation , J. Therm. Stresses vol. 33 , no. 4 , pp. 305 – 317 , 2010 .
   Web of Science ®Google Scholar
• F. Passarella , and V. Zampoli , Reciprocal, and Variational Principles in Micropolar Thermoelasticity of Type II , Acta Mech. , vol. 216 , no. 1–4 , pp. 29 – 36 , 2011 .
   Google Scholar
• F. Passarella , V. Tibullo , and V. Zampoli , On the Heat-flux Dependent Thermoelasticity for Micropolar Porous Media , J. Therm. Stresses vol. 34 , no. 8 , pp. 778 – 794 , 2011 .
   Web of Science ®Google Scholar
• F. Passarella , V. Tibullo , and V. Zampoli , On the Strong Ellipticity for Orthotropic Micropolar Elastic Bodies in a Plane Strain State , Mech. Res. Commun. , vol. 38 , no. 7 , pp. 512 – 517 , 2011 .
   Google Scholar
• M. A. Goodman and S. C. Cowin , A Continuum Theory for Granular Materials , Arch. Rat. Mech. Anal. , vol. 44 , p. 249 , 1972 .
   Web of Science ®Google Scholar
• J. W. Nunziato and S. C. Cowin , A Nonlinear Theory of Elastic Materials with Voids , Arch. Rat. Mech. Anal. , vol. 72 , pp. 175 – 201 , 1979 .
   Web of Science ®Google Scholar
• S. C. Cowin and J. W. Nunziato , Linear Elastic Materials with Voids , J. Elast. vol. 13 , pp. 125 – 147 , 1983 .
   Web of Science ®Google Scholar
• E. Scarpetta , On the Fundamental Solutions in Micropolar Elasticity with Voids , Acta Mech. , vol. 82 , no. 3–4 , pp. 151 – 158 , 1990 .
   Google Scholar
• M. Ciarletta and F. Passarella , Some Results in the Dynamics of Porous Elastic Mixtures , Int. J. Eng. Sci. , vol. 41 , no. 9 , pp. 995 – 1018 , 2003 .
   Google Scholar
• M. Ciarletta , F. Passarella , and M. Svanadze , Plane Waves and Uniqueness Theorems in the Coupled Linear Theory of Elasticity for Solids with Double Porosity , Journal of Elasticity , pp. 1 – 14 , 2013 , doi: 10.1007/s10659-012-9426-x .
   Google Scholar
• G. Iovane , F. Passarella , Saint-Venant's Principle in Dynamic Porous Thermoelastic Media with Memory for Heat Flux , J. Therm. Stresses , vol. 27 , no. 11 , pp. 983 – 999 , 2004 .
   Web of Science ®Google Scholar
• M. Ciarletta , S. Chirita , and F. Passarella , Some Results on the Spatial Behaviour in Linear Porous Elasticity , Arch. Mech. vol. 57 , no. 1 , pp. 43 – 65 , 2005 .
   Google Scholar
• S. Chirita , M. Ciarletta , and B. Straughan , Structural Stability in Porous Elasticity , Proc. Roy. Soc. A , vol. 462 , no. 2073 , pp. 2593 – 2605 , 2006 .
   Google Scholar
• S. Chirita and M. Ciarletta , On the Structural Stability of Thermoelastic Model of Porous Media , Math. Meth. Appl. Sci. , vol. 31 , no. 1 , pp. 19 – 34 , 2008 .
   Google Scholar
• M. Ciarletta , B. Straughan , and V. Tibullo , Modelling Boundary and Nonlinear Effects in Porous Media Flow , Nonlin. Anal.-Real World App. , vol. 12 , no. 5 , pp. 2839 – 2843 , 2011 .
   Google Scholar
• L. Brun , Sur l'unicité en Thermoelasticité Dynamique et Diverses Expressions Analogues à la Formule de Clapeyron, C R Acad. Sci. Paris vol. 261, pp. 2584–2587, 1965.
   Google Scholar
• L. Brun , Méthodes Énergétiques Dans les Systèmes Évolutifs Linéaires, Première Partie: Separation des Énergies, Deuxième partie: Théorèmes d'unicité , J. Méc. vol. 8 , pp. 125 – 166 , 167–192 , 1969 .
   Google Scholar
• R. J. Knops and L. E. Payne , On Uniqueness and Continuous Data Dependence in Dynamical Problems of Linear Thermoelasticity , Int. J. Solids Struct. vol. 6 , pp. 1173 – 1184 , 1970 .
   Google Scholar
• H. A. Levine , On a Theorem of Knops and Payne in Dynamical Thermoelasticity , Arch. Ration. Mech. Anal. vol. 38 , pp. 290 – 307 , 1970 .
   Web of Science ®Google Scholar
• N. S. Wilkes , Continuous Dependence and Instability in Linear Thermoelasticity . SIAM J. Appl. Math. vol. 11 , pp. 292 – 299 , 1980 .
   Web of Science ®Google Scholar
• S. Rionero and S. Chirita , The Lagrange Identity Method in Linear Thermoelasticity , Int. J. Eng. Sci. vol. 25 , pp. 935 – 947 , 1987 .
   Web of Science ®Google Scholar
• D. Iesan , On Some Theorems in Thermoelastodynamics , Rev. Roum. Sci. Tech., Sér. Méc. Appl. vol. 34 , pp. 101 – 111 , 1989 .
   Google Scholar
• D. Iesan , Reciprocity, Uniqueness, and Minimum Principles in the Dynamic Theory of Thermoelasticity . J. Therm. Stresses , vol. 12 , pp. 465 – 482 , 1989 .
   Web of Science ®Google Scholar
• F. Passarella and V. Zampoli , Some Results on the Spatial Behaviour for Elastic Mixtures , Europ. J. Mech.—A/Solids , vol. 25 , no. 6 , pp. 1031 – 1040 , 2006 .
   Google Scholar
• F. Passarella and V. Zampoli , Some Exponential Decay Estimates for Thermoelastic Mixtures , J. Therm. Stresses , vol. 30 , no. 1 , pp. 25 – 41 , 2007 .
   Web of Science ®Google Scholar
• F. Passarella and V. Zampoli , On the Exponential Decay for Viscoelastic Mixtures , Arch. Mech. , vol. 59 , no. 2 , pp. 97 – 117 , 2007 .
   Google Scholar
• V. Tibullo and V. Zampoli , A Uniqueness Result for the Cattaneo-Christov Heat Conduction Model Applied to Incompressible Fluids , Mech. Res. Commun. , vol. 38 , no. 1 , pp. 77 – 79 , 2011 .
   Web of Science ®Google Scholar
• F. Passarella , V. Tibullo , and V. Zampoli , On Microstretch Thermoviscoelastic Composite Materials , Euro. J. Mech.—A/Solids , vol. 37 , pp. 294 – 303 , 2013 .
   Web of Science ®Google Scholar
• D. Iesan , A Theory of Thermoelastic Materials with Voids , Acta Mech. , vol. 60 , pp. 67 – 89 , 1986 .
   Web of Science ®Google Scholar
• S. Chirita , On the Final Boundary Value Problems in Linear Thermoelasticity , Meccanica , Published online 25 July 2012 , doi: 10.1007/s11012-012-9570-1 .
   Google Scholar