Abstract wave equations with generalized Wentzell boundary conditions

Journal of Differential Equations

Volumn 207, Issue 1, 2004, Pages 1-20

  Bátkai, András ^a   Engel, Klaus Jochen ^b  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^b UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

Operator matrices; Perturbation; Phase spaces; Sine and cosine families; Wave equations; Wentzell boundary conditions

Indexed keywords

EID: 8644235109     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2003.12.005     Document Type: Article

References (36)

1. W. Arendt C.J.K. Batty M. Hieber F. Neubrander Vector-valued Laplace transforms and Cauchy problems, Monographs in Mathematics, vol. 96, Birkhäuser Verlag, Basel, 2001
2. W. Arendt H. Kellermann Integrated solutions of Volterra integrodifferential equations and applications in: G. Da Prato, M. Iannelli (Eds.), Volterra Integro-Differential Equations in Banach Spaces and Applications (Proceedings Trento 1987), Pitman Research Notes in Mathematics, vol. 190, Longman, New York 1989 pp. 21-51
3. W. Arendt G. Metafune D. Pallara S. Romanelli The Laplacian with Wentzell-Robin boundary conditions on spaces of continuous functions Semigroup Forum 67 2003 247-261
4. 1 (Ω) generated by degenerate elliptic operators Semigroup Forum 62 2001 317-328
5. M. Campiti G. Metafune Ventcel's boundary conditions and analytic semigroups Arch. Math. 70 1998 377-390
6. M. Campiti G. Metafune D. Pallara S. Romanelli Semigroups for ordinary differential operators in: K.-J. Engel, R. Nagel (Eds.), One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, vol. 194, Springer, Berlin, 2000 pp. 383-404
7. V. Casarino K.-J. Engel G. Nickel S. Piazzera Decoupling techniques for wave equations with dynamic boundary conditions, Discrete Contin. Dynamics Systems Ser. A (2004), to appear (see also: Tübinger Berichte zur Funktionalanalysis (2001/02), 35-44)
8. 0 -semigroups generated by differential operators satisfying Ventcel's boundary conditions Nederl. Akad. Wetensch. Indag. Math. 48 1986 379-387
9. K.-J. Engel Analyticity of semigroups generated by operators with generalized Wentzell boundary conditions, 2003, preprint
10. K.-J. Engel The Laplacian on C (Ω̄) with generalized Wentzell boundary conditions Arch. Math. 81 2003 548-558
11. K.-J. Engel Second order differential operators on C[0,1] with Wentzell-Robin boundary conditions, in: G. Ruiz Goldstein, R. Nagel, S. Romanelli (Eds.), Evolution Equations: Proceedings in Honor of J.A. Goldstein's 60th Birthday, Lecture Notes in Pure and Applied Mathematics, no. 234, Marcel Dekker, New York, 2003 pp. 159-165
12. K.-J. Engel R. Nagel One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics vol. 194, Springer, Berlin, 2000
13. H.O. Fattorini Second order linear differential equations in Banach spaces, North-Holland Mathematics Studies, vol. 108, North-Holland, Amsterdam, 1985
14. 0 -semigroups generated by second order differential operators with generalized Wentzell boundary conditions Proc. Amer. Math. Soc. 128 2000 1981-1989
15. A. Favini G. Ruiz Goldstein J.A. Goldstein S. Romanelli Generalized Wentzell boundary conditions and analytic semigroups in C [ 0,1 ] , in: A.V. Balakrishnan (Ed.), Semigroups of Operators: Theory and Applications (Proceedings Newport Beach, CA, 1998), Progress in Nonlinear Differential Equations and Applications, vol. 42, Birkhäuser Verlag, Basel, 2000 pp. 125-130
16. A. Favini G. Ruiz Goldstein J.A. Goldstein S. Romanelli The one dimensional wave equation with generalized Wentzell boundary conditions in: S. Aicovici, N. Pavel (Eds.), Differential Equations and Control Theory, Lecture Notes in Pure and Applied Mathematics vol. 225, Marcel Dekker, New York, 2001, pp. 139-145 (see also: Tübinger Berichte zur Funktionalanalysis 9 (1999/2000), 162-168)
17. 1.p Math. Nachr. 238 2002 78-102
18. A. Favini G. Ruiz Goldstein J.A. Goldstein S. Romanelli The heat equation with generalized Wentzell boundary condition J. Evol. Equ. 2 2002 1-19
19. A. Favini A. Yagi Degenerate differential equations in Banach Spaces, Pure and Applied Mathematics vol. 215 1999 Marcel Dekker New York
20. W. Feller Diffusion processes in one dimension Trans. Amer. Math. Soc. 97 1954 1-31
21. C.G. Gal G. Ruiz Goldstein J.A. Goldstein Oscillatory boundary conditions for acoustic wave equations, J. Evol. Equ. 3 2003 623-635
22. J.A. Goldstein Semigroups of Operators and Applications 1985 Oxford University Press Oxford
23. G. Greiner Perturbing the boundary conditions of a generator Houston J. Math. 13 1987 213-229
24. H. Kellermann M. Hieber Integrated semigroups J. Funct. Anal. 84 1989 160-180
25. H. Langer L. Partzsch D. Schütze Über verallgemeinerte gewöhnliche Differentialoperatoren mit nichtlokalen Randbedingungen und die von ihnen erzeugten Markov-Prozesse Publ. Res. Inst. Math. Sci. 7 1971/72 659-702
26. P. Mandl Analytical Treatment of One-dimensional Markov-processes 1968 Springer Berlin
27. G. Metafune Analyticity for some degenerate one-dimensional evolution equations Stud. Math. 127 1998 251-276
28. M. Sova Cosine operator functions Rozprawy Mat. 49 1966 1-46
29. K. Taira A. Favini S. Romanelli Feller semigroups and degenerate elliptic operators with Wentzell boundary conditions Stud. Math. 145 2001 17-53
30. T. Ueno Wave equation with Wentzell's boundary condition and a related semigroup on the boundary. I, Proc. Japan Acad. 49 (1973) 672-677
31. T. Ueno II, Proc. Japan Acad. 50 (1974) 281-286
32. M. Warma Wentzell-Robin boundary conditions on C[0,1] Semigroup Forum 66 2003 162-170
33. M. Watanabe Cosine families of operators and applications, in: A. Favini, E. Obrecht (Eds.), Differential Equations in Banach Spaces (Proceedings Bologna 1985), Lecture Notes in Mathematics, vol. 1223, Springer, Berlin, 1986, pp. 278-292
34. A.D. Wentzell On boundary conditions for multi-dimensional diffusion processes Theory Probab. Appl. 4 1959 164-177
35. T.-J. Xiao J. Liang The Cauchy problem for higher-order abstract differential equations, Lecture Notes in Mathematics, vol. 1701, Springer, Berlin 1998
36. T.-J. Xiao J. Liang Wave equations with generalized Wentzell boundary conditions Math. Ann. 327 2003 351-363