Hostname: page-component-7479d7b7d-t6hkb Total loading time: 0 Render date: 2024-07-08T13:32:31.301Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear parabolic equations with venttsel initial boundary conditions

Published online by Cambridge University Press:  17 April 2009

Yi Zeng  and
Yousong Luo
Yi Zeng
Affiliation:
Department of MathematicsRoyal Melbourne Institute of TechnologyGPO Box 2476V Melbourne, Vic. 3001, Australia
Yousong Luo
Affiliation:
Department of MathematicsRoyal Melbourne Institute of TechnologyGPO Box 2476V Melbourne, Vic. 3001, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Schauder estimates for solutions of linear second order parabolic equations with Venttsel initial boundary conditions are proved, and existence and uniqueness of classical solutions under such an initial boundary condition are established. An application to an engineering problem is also given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 3 , December 1994 , pp. 465 - 479
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Cannon, J.R. and Meyer, G.H., ‘On diffusion in a fractured medium’, SIAM J. Appl. Math. 3 (1971), 434–448.CrossRefGoogle Scholar
[2]Friedman, A., Partial differential equations of parabolic type (Prentice-Hall, Inc., Englewood Cliffs NJ, London, 1964).Google Scholar
[3]Gilbarg, D. and Trudinger, N.S., Elliptic partial differential equations of second order, Second Edition (Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983).Google Scholar
[4]Korman, P., ‘Existence of solutions for a class of semilinear noncoercive problems’, Nonlinear Anal. 10 (1986), 1471–1476.CrossRefGoogle Scholar
[5]Luo, Y. and Trudinger, N.S., ‘Linear second order elliptic equations with Venttsel boundary conditions’, Proc. Roy. Soc. Edinburgh Sect. A 118 (1991), 193–270.CrossRefGoogle Scholar
[6]Luo, Y., ‘On the quasilinear elliptic Venttsel boundary value problem’, Nonlinear Anal. 16 (1991), 761–769.CrossRefGoogle Scholar