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Applicable Analysis
An International Journal
Volume 83, 2004 - Issue 2
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Original Articles

On a nonstandard problem for heat conduction in a cylinder

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Pages 125-133 | Received 09 May 2003, Published online: 25 Jan 2007

References

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  • Ames , KA and Payne , LE . 1999 . Continuous dependence on modeling for some well-posed perturbations of the backward heat equation . J. Inequalities Appl. , 3 : 51 – 64 .
  • Ames KA Payne LE Schaefer PW Energy and pointwise bounds in some nonstandard parabolic problems Proc. Royal Soc. Edinburgh (to appear)
  • Clark G Oppenheimer C 1994 Quasireversibility methods for non-well-posed problems Elect. J. Diff. Eq. No. 8 1 9
  • Flavin , J , Knops , RJ and Payne , LE . 1989 . Decay estimates for the constrained elastic cylinder of variable cross section . Q. Appl. Math. , 47 : 325 – 350 .
  • Hersch , J . 1960 . Sur la fréquence fondamentale d’une membrane vibrante: évaluations par défaut et principe du maximum . ZAMP , 11 : 387 – 413 .
  • Horgan , CO , Payne , LE and Wheeler , LT . 1984 . Spatial decay estimates in transient heat conduction . Q. Appl. Math. , 42 : 119 – 127 .
  • Knops RJ Payne LE Alternative spatial growth and decay for constrained motion in an elastic cylinder J. Math. Mech. of Solids (to appear)
  • Payne , LE and Philippin , GA . 2000 . On the spatial decay of solutions to a quasilinear parabolic initial-boundary value problem and their derivatives . SIAM J. Math. Anal. , 32 : 291 – 303 .
  • Payne , LE and Schaefer , PW . 2001 . Energy bounds for some nonstandard problems in partial differential equations . J. Math. Anal. Appl. , 273 : 75 – 92 .
  • Protter MH Weinberger HF 1967 Maximum Principles in Differential Equations, Prentice Hall, Inc. Englewood Cliffs NJ
  • Showalter RE 1985 Cauchy problem for hyper-parabolic partial differential equations Trends in the Theory and Practice of Non-Linear Analysis, Elsevier New York NY 421 425

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