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Semi-linear elliptic and elliptic-parabolic equations with Wentzell boundary conditions and $L^1$-data
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Goldstein-Wentzell boundary conditions: Recent results with Jerry and Gisèle Goldstein
| 1. | Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, via E. Orabona 4, 70125 Bari, Italy |
References:
| [1] |
T. Clarke, G. R. Goldstein, J. A. Goldstein and S. Romanelli, The Wentzell telegraph equation: Asymptotics and continuous dependence on the boundary conditions, Comm. Appl. Anal., 15 (2011), 313-324. |
| [2] |
G. M. Coclite, A. Favini, C. G. Gal, G. R. Goldstein, J. A. Goldstein, E. Obrecht and S. Romanelli, The role of Wentzell boundary conditions in linear and nonlinear analysis, in "Advances in Nonlinear Analysis: Theory, Methods and Applications" (ed. S. Sivasundaran), Math. Probl. Eng. Aerosp. Sci., 3, Cambridge Scientific Publishers, Cambridge, (2009), 277-289. |
| [3] |
G. M. Coclite, A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, Continuous dependence on the boundary parameters for the Wentzell Laplacian, Semigroup Forum, 77 (2008), 101-108 |
| [4] |
G. M. Coclite, A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, Continuous dependence in hyperbolic problems with Wentzell boundary conditions, Comm. Pure Appl. Math., to appear. |
| [5] |
K.-J. Engel and G. Fragnelli, Analyticity of semigroups generated by operators with generalized Wentzell boundary conditions, Adv. Diff. Eqns., 10 (2005), 1301-1320. |
| [6] |
A. Favini, G. R. Goldstein, J. A. Goldstein, E. Obrecht and S. Romanelli, Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem, Math. Nachr., 283 (2010), 504-521. |
| [7] |
A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, $C_0$-semigroups generated by second order differential operators with general Wentzell boundary conditions, Proc. Amer. Math. Soc., 128 (2000), 1981-1989. |
| [8] |
A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, The heat equation with generalized Wentzell boundary condition, J. Evol. Equ., 2 (2002), 1-19. |
| [9] |
G. R. Goldstein, Derivation and physical interpretation of general boundary conditions, Adv. Diff. Eqns., 11 (2006), 457-480. |
| [10] |
J. A. Goldstein, "Semigroups of Linear Operators and Applications," Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1985. |
| [11] |
J. A. Goldstein, On the convergence and approximation of cosine functions, Aeq. Math., 10 (1974), 201-205. |
| [12] |
P. D. Lax, "Functional Analysis," Wiley-Interscience, New York, 2002. |
show all references
References:
| [1] |
T. Clarke, G. R. Goldstein, J. A. Goldstein and S. Romanelli, The Wentzell telegraph equation: Asymptotics and continuous dependence on the boundary conditions, Comm. Appl. Anal., 15 (2011), 313-324. |
| [2] |
G. M. Coclite, A. Favini, C. G. Gal, G. R. Goldstein, J. A. Goldstein, E. Obrecht and S. Romanelli, The role of Wentzell boundary conditions in linear and nonlinear analysis, in "Advances in Nonlinear Analysis: Theory, Methods and Applications" (ed. S. Sivasundaran), Math. Probl. Eng. Aerosp. Sci., 3, Cambridge Scientific Publishers, Cambridge, (2009), 277-289. |
| [3] |
G. M. Coclite, A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, Continuous dependence on the boundary parameters for the Wentzell Laplacian, Semigroup Forum, 77 (2008), 101-108 |
| [4] |
G. M. Coclite, A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, Continuous dependence in hyperbolic problems with Wentzell boundary conditions, Comm. Pure Appl. Math., to appear. |
| [5] |
K.-J. Engel and G. Fragnelli, Analyticity of semigroups generated by operators with generalized Wentzell boundary conditions, Adv. Diff. Eqns., 10 (2005), 1301-1320. |
| [6] |
A. Favini, G. R. Goldstein, J. A. Goldstein, E. Obrecht and S. Romanelli, Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem, Math. Nachr., 283 (2010), 504-521. |
| [7] |
A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, $C_0$-semigroups generated by second order differential operators with general Wentzell boundary conditions, Proc. Amer. Math. Soc., 128 (2000), 1981-1989. |
| [8] |
A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, The heat equation with generalized Wentzell boundary condition, J. Evol. Equ., 2 (2002), 1-19. |
| [9] |
G. R. Goldstein, Derivation and physical interpretation of general boundary conditions, Adv. Diff. Eqns., 11 (2006), 457-480. |
| [10] |
J. A. Goldstein, "Semigroups of Linear Operators and Applications," Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1985. |
| [11] |
J. A. Goldstein, On the convergence and approximation of cosine functions, Aeq. Math., 10 (1974), 201-205. |
| [12] |
P. D. Lax, "Functional Analysis," Wiley-Interscience, New York, 2002. |
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