- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 202373, 4 pages
On the Stability of Heat Equation
1Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia
2Mathematics Section, College of Science and Technology, Hongik University, Sejong 339-701, Republic of Korea
Received 19 June 2013; Accepted 18 September 2013
Academic Editor: Bing Xu
Copyright © 2013 Balázs Hegyi and Soon-Mo Jung. 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.
- C. Alsina and R. Ger, “On some inequalities and stability results related to the exponential function,” Journal of Inequalities and Applications, vol. 2, no. 4, pp. 373–380, 1998.
- S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, River Edge, NJ, USA, 2002.
- D. H. Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United States of America, vol. 27, pp. 222–224, 1941.
- D. H. Hyers, G. Isac, and T. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, Boston, Mass, USA, 1998.
- S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, vol. 48 of Springer Optimization and Its Applications, Springer, New York, NY, USA, 2011.
- T. M. Rassias, “On the stability of the linear mapping in Banach spaces,” Proceedings of the American Mathematical Society, vol. 72, no. 2, pp. 297–300, 1978.
- S. M. Ulam, Problems in Modern Mathematics, John Wiley & Sons, New York, NY, USA, 1964.
- M. Obłoza, “Hyers stability of the linear differential equation,” Rocznik Naukowo-Dydaktyczny. Prace Matematyczne, no. 13, pp. 259–270, 1993.
- M. Obłoza, “Connections between Hyers and Lyapunov stability of the ordinary differential equations,” Rocznik Naukowo-Dydaktyczny. Prace Matematyczne, no. 14, pp. 141–146, 1997.
- T. Miura, S.-M. Jung, and S.-E. Takahasi, “Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations ,” Journal of the Korean Mathematical Society, vol. 41, no. 6, pp. 995–1005, 2004.
- S.-E. Takahasi, T. Miura, and S. Miyajima, “On the Hyers-Ulam stability of the Banach space-valued differential equation ,” Bulletin of the Korean Mathematical Society, vol. 39, no. 2, pp. 309–315, 2002.
- S.-M. Jung and K.-S. Lee, “Hyers-Ulam stability of first order linear partial differential equations with constant coefficients,” Mathematical Inequalities & Applications, vol. 10, no. 2, pp. 261–266, 2007.
- A. Prástaro and T. M. Rassias, “Ulam stability in geometry of PDE's,” Nonlinear Functional Analysis and Applications, vol. 8, no. 2, pp. 259–278, 2003.
- N. Lungu and D. Popa, “Hyers-Ulam stability of a first order partial differential equation,” Journal of Mathematical Analysis and Applications, vol. 385, no. 1, pp. 86–91, 2012.
- B. Hegyi and S.-M. Jung, “On the stability of Laplace's equation,” Applied Mathematics Letters, vol. 26, no. 5, pp. 549–552, 2013.
- L. C. Evans, Partial Differential Equations, vol. 19 of Graduate Studies in Mathematics, American Mathematical Society, 1998.
- S.-M. Jung, “Hyers-Ulam stability of linear differential equations of first order. II,” Applied Mathematics Letters, vol. 19, no. 9, pp. 854–858, 2006.