| Title | THE WENTZELL TELEGRAPH EQUATION: ASYMPTOTICS AND CONTINUOUS DEPENDENCE ON THE BOUNDARY CONDITIONS |
| Publication Type | Journal Article |
| Year of Publication | 2011 |
| Authors | CLARKE, TED, GOLDSTEIN, GISELERUIZ, GOLDSTEIN, JEROMEA, ROMANELLI, SILVIA |
| Secondary Title | Communications in Applied Analysis |
| Volume | 15 |
| Issue | 3 |
| Start Page | 313 |
| Pagination | 324 |
| Date Published | 08/2011 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 35B30., 35B40, 47D06 |
| Abstract | Solutions of the telegraph equation in many unbounded domains are shown to be asymptotically equal to solutions of the corresponding heat equation. This works for many boundary conditions, including general Wentzell boundary conditions. Continuous dependence on the boundary conditions is also shown.
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| URL | http://www.acadsol.eu/en/articles/15/3/4.pdf |
| Short Title | THE WENTZELL TELEGRAPH EQUATION |
| Refereed Designation | Refereed |
| Full Text | REFERENCES[1] T. Clarke, E.C. Eckstein and J.A. Goldstein, Asymptotics analysis of the abstract telegraph equation, Diff. Int. Eqns. 21 (2008), 433–442.
[2] G.M. Coclite, A. Favini, C.G. Gal, G. Ruiz Goldstein, J.A. Goldstein, E. Obrecht and S. Romanelli, The role of Wentzell boundary conditions in linear and nonlinear analysis, Advances in Nonlinear Analysis: Theory, Methods and Applications (S. Sivasundaran Ed.), vol. 3, pages 279–292, Cambridge Scientific Publishers Ltd., Cambridge, 2009. [3] G. M. Coclite, A. Favini, G. Ruiz Goldstein, J. A. Goldstein, and S. Romanelli, Continuous dependence on the boundary parameters for the Wentzell Laplacian, Semigroup Forum 77 (2008), 101–108. [4] A. Favini, G. Ruiz Goldstein, J.A. Goldstein and S. Romanelli, The heat equation with generalized Wentzell boundary condition, J. Evol. Equ. 2 (2002), 1–19. [5] J.A. Goldstein, On the convergence and approximation of cosine functions, Aeq. Math. 10 (1974), 201–205. [6] J.A. Goldstein, Semigroups of Linear Operators and Applications, Oxford University Press, Oxford, 1985. [7] P.D. Lax, Functional Analysis, Wiley-Interscience, New York, 2002. |