Some alternative results for the nonlinear viscoelasticity equations

References

• Horgan , CO and Knowles , JK . Recent development concerning Saint-Venant's principle, Adv. Appl. Mech. 23 (1983), pp. 179–269.
   Google Scholar
• Horgan , CO . 1989 . Recent development concerning Saint-Venant's principle: An update . Appl. Mech. Rev. , 42 : 295 – 303 .
   Google Scholar
• Horgan , CO . 1996 . Recent development concerning Saint-Venant's principle: An second update . Appl. Mech. Rev. , 49 : 101 – 111 .
   Google Scholar
• Boley , BA . 1958 . Some observations on Saint-Venant principle, Third U.S. Congress of Applied Mechanics , 259 – 264 . New York : ASME .
   Google Scholar
• Knowles , JW . 1971 . On the spatial decay of solutions of the heat equation . Z. Angew. Math. Phys. , 22 : 1050 – 1056 .
   Web of Science ®Google Scholar
• Lin , C . 1992 . Spatial decay estimates and energy bounds for the Stokes flow equations . SACCM , 2 : 249 – 264 .
   Google Scholar
• Lin , C and Payne , LE . 2004 . Spatial decay bounds in time dependent pipe flow of an incompressible viscous fluid . SIAM J. Appl. Math. , 65 : 458 – 474 .
   Google Scholar
• Lin , C and Payne , LE . 2004 . Spatial decay bounds in the channel flow of an incompressible viscous fluid . Math. Models. Meth. Appl. Sci. , 14 : 795 – 818 .
   Google Scholar
• Payne , LE and Song , JC . 2005 . Improved spatial decay bounds in generalized heat conduction . Z. Angew. Math. Phy. , 56 : 805 – 820 .
   Google Scholar
• Song , JC . 2003 . Improved decay estimates in time-dependent Stokes flow . J. Math. Anal. Appl. , 288 : 505 – 517 .
   Google Scholar
• Horgan , CO and Payne , LE . 1980 . Decay estimates for a class of nonlinear boundary value problems in two dimensions . SIAM. J. Math. Anal. , 20 : 782 – 788 .
   Google Scholar
• Flavin , JN , Knops , RJ and Payne , LE . 1989 . Decay estimates for the constrained elastic cylinder of variable cross section . Quart. Appl. Math. , 47 : 325 – 350 .
   Web of Science ®Google Scholar
• Lin , C and Payne , LE . 1994 . A Phragmén-Lindelöf type results for second order quasi-linear equation in R2 . Z. Angew. Math. Phy. , 45 : 294 – 311 .
   Google Scholar
• Liu , Y and Lin , C . 2006 . Phragmén–Lindelöf-type alternative results for the Stokes flow equation . Math. Inequal. Appl. , 9 : 671 – 694 .
   Google Scholar
• Payne , LE and Schaefer , PW . 1994 . Some Phragmén–Lindelöf-type alternative results for the biharmonic equation . Z. Angew. Math. Phy. , 45 : 414 – 432 .
   Google Scholar
• Horgan , CO and Payne , LE . 1993 . Phragmén–Lindelöf-type results for harmonic functions with nonlinear boundary conditions . Arch. Rational Mech. Anal. , 122 : 123 – 144 .
   Google Scholar
• Knops , RJ and Payne , LE . 1983 . A Saint-Venant principle for nonlinear elasticity . Arch. Rational Mech. Anal. , 81 : 1 – 12 .
   Google Scholar
• Borrelli , A and Patria , MC . 1996 . Energy bounds in dynamical problems for a semi-infinite magnetoelastic beam . J. Appl. Math. Phys. , 47 : 880 – 893 .
   Google Scholar
• Chirita , S and Quintallina , R . 1996 . Saint-Venant's principle in linear elastodynamics . J. Elasticity , 42 : 201 – 215 .
   Web of Science ®Google Scholar
• Chirita , S and Quintallina , R . 1996 . Spatial decay estimates of Saint-Venant's type in generalized thermoelasticity . Int. J. Eng. Sci. , 34 : 299 – 311 .
   Web of Science ®Google Scholar
• Diaz , JI and Quintallina , R . 2002 . Spatial and continuous dependence estimates in linear viscoelasticity . J. Math. Anal. Appl. , 273 : 1 – 16 .
   Google Scholar
• Quintallina , R . 1996 . Spatial decay estimates for hyperbolic heat equation . SIAM J. Math. Anal. , 27 : 78 – 91 .
   Google Scholar
• Quintallina , R . 1996 . Phragmén–Lindelöf alternative for linear equations of the anti-plane shear dynamic problem in viscoelasticity . Dyn. Contin. Discr. Impulsive Syst. , 2 : 423 – 435 .
   Google Scholar
• Quintallina , R . 1998 . Phragmén–Lindelöf alternative in nonlinear viscoelasticity . Nonlinear Anal. , 34 : 7 – 16 .
   Google Scholar
• Ames , KA . 2000 . Continuous dependence on modelling and non-existence for a Ginzburg–Laudau Equation . Math. Mech. Appl. Sci. , 23 : 1537 – 1550 .
   Web of Science ®Google Scholar
• Ames , KA and Straughan , B . 1997 . Non-standard and Improperly Posed Problems, Vol. 194, Mathematics in Science and Engineering Series , San Diego : Academic press .
   Google Scholar
• Evans , LC . 1998 . Partial Differential Equations , Providence, RI : American Mathematical Society .
   Google Scholar
• Flavin , JN and Rionero , S . 1996 . Qualitative Estimates for Partial Differential Equation: An Introduction , Boca, Raton : CRC Press .
   Google Scholar
• Quintallina , R . 2006 . On the spatial blow-up and decay for some nonlinear parabolic equations with nonlinear boundary conditions . Z. Angew. Math. Phys. , 57 : 595 – 603 .
   Google Scholar