- Volume 13 Issue 2
This paper investigates history and modern developments concerning spatial decay estimates for solutions in a semi-infinite cylinder or strip, in which model equations are defined with appropriate homogeneous lateral boundary conditions and initial conditions but left end boundary data are assumed. Our aim is to show this Saint-Venant type decay rate dependent critically on the Poincare constant resulting from characterizing variational principles.
- Proc. 3rd U.S. Nat. Cong. Appl. Mech. Some observations on Saint-Venant's principle Boley, B.A.
- Z. angew. Math. Phys.(ZAMP) v.22 On the spatial decay os solutions of the heat equation Knowles, J.K.
- Math. Meth. Appl. Sci. v.21 Bounds and decay results for some second-order semilinear elliptic problems Payne, L.E.;P.W. Schaefer;J.C. Song
- Math. Models Meth. Appl. Sci. Spatial decay for solutions of Cauchy problems for perturbed heat equations Song, J.C.
- J. Korean Math. Soc. Decay estimates for steady magnetohydrodynamics equations in a semi-infinite cylinder Song, J.C.
- SIAM J. Math. Anal. v.24 Spatial decay estimates in time dependent Stokes flow Ames, K.A.;L.E. Payne;P.W. Schaefer
- Quart. appl. Math. v.50 Saint-Venant's principle for a theory of non-linear plane elasticity Horgan, C.O.;L.E. Payne
- SACCM v.2 Spatial decay estimates and energy bounds for the Stokes flow equation Lin, C.
- Arch. Rational Mech. Anal. v.104 Exponential decay estimates for solutions of the von Karman equations on a semi-infinite strip Vafeades, P.;C.O. Horgan
- Advances in Applied Mechanics v.23 Recent developments concerning Saint-Venant's principle Horgan, C.O.;J.K. Knowles;T.Y. Wu(ed.);J.W. Hutchinson(ed.)
- Z. angew. Math. Phys. (ZAMP) Spatial decay for a model of double diffusive convection in Darcy and Brinkman flows Payne, L.E.;J.C. Song
- Arch. Rational Mech. Anal. v.122 Phragmen-Lindelof type results for harmonic functions with nonlinear boundary conditions Horgan, C.O.;L.E. Payne
- Quart. Appl. Math. v.52 Energy estimates for the biharmonic equations in three dimensions Lin, C.
- SIAM J. Appl. Math. v.25 Spatial decay estimate for the Navier-Stokes equations with application to the problem of entry flow Horgan, C.O.;L.T. Wheeler
- Quart. Appl. Math. v.42 Spatial decay estimates in transient heat conduction Horgan, C.O.;L.E. Payne;L.T. Wheeler
- Appl. Mech. Rev. v.42 Recent developments concerning Saint-Venant's principle: an update Horgan, C.O.
- Nonlinear Analysis v.35 Growth and decay results in heat conduction problems with nonlinear boundary conditions Payne, L.E.;P.W. Schaefer;J.C. Song
- Spatial decay bounds for the Forchheimer equations Payne, L.E.;J.C. Song
- J. Math. Anal. Appl. v.207 Decay estimates in steady semi-infinite thermal pipe flow Song, J.C.
- J. Korean Math. Anal. v.35 Phragmen-Lindelof and continuous dependence type results in generalized dissipative heat conduction Song, J.C.;D.S. Yoon
- Continuum Mech. Thermodyn. v.9 Spatial decay estimates for the Brinkman and Darcy flows in a semi-infinite cylinder Payne, L.E.;J.C. Song
- Appl. Mech. Rev. v.49 Recent developments concerning Saint-Venant's principle: a second update Horgan, C.O.
- Quart. Appl. Math. v.47 Decay estimates for the biharmonic equation with applications to Saint-Venant's principle in plane elasticity and Stokes flows Horgan, C.O.
- SIAM J. Math. Anal. v.27 A spatial decay estimate for the hyperbolic heat equation Quintanilla, R.
- Spatial decay estimates in time-dependent double diffusive Darcy plane flow Song, J.C.
- Z. angew. Math. Phys. (ZAMP) v.47 Phragmen-Lindelof and continuous dependence type results in generalized heat conduction Payne, L.E.;J.C. Song
- SIAM J. Math. Anal. v.5 Exponential decay of functionals of solutions of a peudoparabolic equation Sigillito, V.G.
- Spatial decay in the pipe flow of a viscous fluid interfacing a porous medium Ames, K.A.;L.E. Payne;J.C. Song
- SIAM J. Math. Anal. v.20 Decay estimates in steady pipe flow Ames, K.A.;L.E. Payne
- Arch. Rational Mech. Anal. v.68 Plane entry flows and energy estimates for the Navier-Stokes Equations Horgan, C.O.