- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 535629, 8 pages
The Initial and Neumann Boundary Value Problem for a Class Parabolic Monge-Ampère Equation
1School of Mathematics, Physics and Biological Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, China
2Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1
Received 26 March 2013; Accepted 11 June 2013
Academic Editor: Sergey Piskarev
Copyright © 2013 Juan Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J.-F. Cossette and P. K. Smolarkiewicz, “A Monge-Ampère enhancement for semi-Lagrangian methods,” Computers & Fluids, vol. 46, pp. 180–185, 2011.
- Z. Liu and Y. He, “Solving the elliptic Monge-Ampère equation by Kansa's method,” Engineering Analysis with Boundary Elements, vol. 37, no. 1, pp. 84–88, 2013.
- J. X. Hong, “The global smooth solutions of Cauchy problems for hyperbolic equation of Monge-Ampère type,” Nonlinear Analysis: Theory, Methods & Applications, vol. 24, no. 12, pp. 1649–1663, 1995.
- E. J. Dean and R. Glowinski, “Numerical methods for fully nonlinear elliptic equations of the Monge-Ampère type,” Computer Methods in Applied Mechanics and Engineering, vol. 195, no. 13-16, pp. 1344–1386, 2006.
- C. E. Gutiérrez, The Monge-Ampère Equation, Birkhäuser, Basel, Switzerland, 2011.
- O. C. Schnürer and K. Smoczyk, “Neumann and second boundary value problems for Hessian and Gauss curvature flows,” Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, vol. 20, no. 6, pp. 1043–1073, 2003.
- P.-L. Lions, N. S. Trudinger, and J. I. E. Urbas, “The Neumann problem for equations of Monge-Ampère type,” Communications on Pure and Applied Mathematics, vol. 39, no. 4, pp. 539–563, 1986.
- J. Urbas, “The second boundary value problem for a class of Hessian equations,” Communications in Partial Differential Equations, vol. 26, no. 5-6, pp. 859–882, 2001.
- J. Urbas, “Oblique boundary value problems for equations of Monge-Ampère type,” Calculus of Variations and Partial Differential Equations, vol. 7, no. 1, pp. 19–39, 1998.
- J. Urbas, “On the second boundary value problem for equations of Monge-Ampère type,” Journal für die Reine und Angewandte Mathematik, vol. 487, pp. 115–124, 1997.
- W. S. Zhou and S. Z. Lian, “The third initial-boundary value problem for an equation of parabolic Monge-Ampère type,” Journal of Jilin University, no. 1, pp. 23–30, 2001.
- J. C. Kuang, Applied Inequalities, Shandong Science and Technology Press, 3rd edition, 2004.
- L. C. Evans, Partial Differential Equations, vol. 19 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 1998.
- Y. Z. Chen, “Some methods of Krylov for the a priori estimation of solutions of fully nonlinear equations,” Advances in Mathematics, vol. 15, no. 1, pp. 63–101, 1986.
- G. C. Dong, “Initial and nonlinear oblique boundary value problems for fully nonlinear parabolic equations,” Journal of Partial Differential Equations. Series A, vol. 1, no. 2, pp. 12–42, 1988.
- O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural’zeva, Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, 1995.
- C. Gerhardt, “Hypersurfaces of prescribed curvature in Lorentzian manifolds,” Indiana University Mathematics Journal, vol. 49, no. 3, pp. 1125–1153, 2000.