Singular evolution problems, regularization, and applications to physics, engineering, and biology

• Autorzy: Günter Lumer
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 38
• Numer: 1
• Strony: 205-216

Daty

wydano

1997

Twórcy

autor

Günter Lumer

• Institute of Mathematics and Informatics, University of Mons-Hainaut, Avenue Maistriau, 15, 7000 Mons, Belgium

Bibliografia

• [1] W. Arendt, Vector-valued Laplace transform and Cauchy problems, Israel J. Math. 59 (1987), 327-352.
• [2] W. Arendt, O. El-Mennaoui and V. Keyantuo, Local integrated semigroups: evolution with jumps of regularity, J. Math. Anal. Appl. 186 (1994), 572-595.
• [4] R. Beals, On the abstract Cauchy problem, J. Funct. Anal. 10 (1972), 281-299.
• [3] R. Beals, Semigroups and abstract Gevrey spaces, ibid. 10 (1972), 300-398.
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• [6] J. Chazarain, Problèmes de Cauchy abstraits et applications à quelques problèmes mixtes, J. Funct. Anal. 7 (1971), 386-446.
• [7] I. Cioranescu, Local convoluted semigroups, to appear.
• [8] I. Cioranescu et G. Lumer, Problèmes d'évolution régularisés par un noyau général K(t). Formule de Duhamel, prolongements, théorèmes de génération, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), 1273-1278.
• [9] I. Cioranescu et G. Lumer, On K(t)-convoluted semigroups, in: Recent Developments in Evolution Equations, Pitman Res. Notes in Math. 324, 1995, 86-93.
• [10] I. Cioranescu and L. Zsidó, ω-Ultradistributions and their applications to operator theory, in: Spectral Theory, Banach Center Publ. 8, 1982, PWN, Warszawa, 77-220.
• [11] Ph. Clément, H. Heijmans et al., One parameter semigroups, CWI Monographs, North-Holland, Amsterdam, 1987.
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• [15] H. Emamirad, Systèmes pseudo différentiels d'évolution bien posés au sens des distributions de Beurling, Boll. Un. Mat. Ital. (6) 1 (1982), 303-322.
• [16] L. Hörmander, An Introduction to Complex Analysis in Several Variables, Van Nostrand, Princeton, 1966.
• [17] H. Kellermann and M. Hieber, Integrated semigroups, J. Funct. Anal. 84 (1989), 160-180.
• [18] V. Keyantuo, The Weierstrass formula and the abstract Cauchy problem, to appear.
• [19] V. Keyantuo, On the boundary value theorem for holomorphic semigroups, preprint Math. Dep. Univ. of Puerto Rico, Rio Piedras.
• [20] H. Komatsu, Ultradistributions I, J. Fac. Sci. Univ. Tokyo Sect. IA 20 (1973), 25-105.
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• [23] G. Lumer, Solutions généralisées et semi-groupes intégrés, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), 577-582.
• [24] G. Lumer, Applications de solutions généralisées et semi-groupes intégrés à des problèmes d'évolution, ibid. 311 (1990), 873-878.
• [25] G. Lumer, Problèmes dissipatifs et analytiques mal posés : solutions et théorie asymptotique, ibid. 312 (1991), 831-836.
• [26] G. Lumer, A (very) direct approach to locally lipschitz integrated semigroups and some new related results oriented towards applications, via generalized solutions, in: LSU Seminar Notes in Functional Analysis and PDES 1990-1991, Louisiana State University, Baton Rouge, 1991, 88-107.
• [27] G. Lumer, Semi-groupes irréguliers et semi-groupes intégrés: application à l'identification de semi-groupes irréguliers analytiques et résultats de génération, C. R. Acad. Sci. Paris Sér. I Math. 314 (1992), 1033-1038.
• [28] G. Lumer, Problèmes d'évolution avec chocs (changements brusques de conditions au bord) et valeurs au bord variables entre chocs consécutifs, ibid. 316 (1993), 41-46.
• [29] G. Lumer, Models for diffusion-type phenomena with abrupt changes in boundary conditions, in Banach space and classical context. Asymptotics under periodic shocks, in: Evolution Equations, Control Theory and Biomathematics, Lecture Notes in Pure Appl. Math. 155, Marcel Dekker, New York, 1994, 337-351.
• [30] G. Lumer, Evolution equations: Solutions for irregular evolution problems via generalized solutions and generalized initial values. Applications to periodic shocks models, Annales Saraviensis 5 (1) (1994), 1-102.
• [31] G. Lumer, Singular problems, generalized solutions, and stability topologies, in: Partial Differential Equations. Models in Physics and Biology, Math. Res. 82, Akademie Verlag, Berlin, 1994, 204-215.
• [32] I. Miyadera, On the generators of exponentially bounded C-semigroups, Proc. Japan Acad. Ser. A Math. Sci. 62 (1986), 239-242.
• [33] F. Neubrander, Integrated semigroups and their applications to the abstract Cauchy problem, Pacific J. Math. 135 (1988), 111-155.
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• [36] E. Sinestrari and W. von Wahl, On the solutions of the first boundary value problem for the linear parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A 108 (1988), 339-355.
• [37] H. Thieme, Semiflows generated by Lipschitz perturbations of non-densely defined operators, Differential Integral Equations 3 (1990), 1035-1066.