Analyticity for some degenerate one-dimensional evolution equations

• Autorzy: G. Metafune
• Języki publikacji: EN

Abstrakty

EN

We study the analyticity of the semigroups generated by some degenerate second order differential operators in the space C([α,β]), where [α,β] is a bounded real interval. The asymptotic behaviour and regularity with respect to the space variable are also investigated.

Kategorie tematyczne

• 35B65: Smoothness and regularity of solutions
• 35B40: Asymptotic behavior of solutions
• 35K65: Degenerate parabolic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 127
• Numer: 3
• Strony: 251-276

Daty

wydano

1998

otrzymano

1996-11-18

poprawiono

1997-08-11

Twórcy

autor

G. Metafune

• Dipartimento di Matematica, Università di Lecce, C.P.193 73100 Lecce, Italy

Bibliografia

• [1] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, 1972.
• [2] S. Angenent, Local existence and regularity for a class of degenerate parabolic equations, Math. Ann. 280 (1988), 465-482.
• [3] A. Attalienti and S. Romanelli, On some classes of analytic semigroups on C([a,b]) related to R- or Γ-admissible mappings, in: Evolution Equations, G. Ferreyra, G. Goldstein and F. Neubrander (eds.), Lecture Notes in Pure and Appl. Math. 168, Dekker, 1995, 29-34.
• [4] H. Brezis, W. Rosenkrantz and B. Singer, On a degenerate elliptic-parabolic equation occurring in the theory of probability, Comm. Pure Appl. Math. 24 (1971), 395-416.
• [5] M. Campiti and G. Metafune, Ventcel's boundary conditions and analytic semigroups, Arch. Math. (Basel), to appear.
• [6] M. Campiti, G. Metafune and D. Pallara, Degenerate self-adjoint evolution equations on the unit interval, Semigroup Forum, to appear.
• [7] P. Clément and C. A. Timmermans, On $C_0$-semigroups generated by differential operators satisfying Ventcel's boundary conditions, Indag. Math. 89 (1986), 379-387.
• [8] A. Favini, J. Goldstein and S. Romanelli, Analytic semigroups on $L_w^p(0,1)$ generated by some classes of second order differential operators, preprint, 1996.
• [9] A. Favini and S. Romanelli, Analytic semigroups on C([0,1]) generated by some classes of second order differential operators, Semigroup Forum, to appear.
• [10] W. Feller, Two singular diffusion problems, Ann. of Math. 54 (1951), 173-182.
• [11] W. Feller, The parabolic differential equations and the associated semi-groups of transformations, ibid. 55 (1952), 468-519.
• [12] G. Fichera, On a degenerate evolution problem, in: Partial Differential Equations with Real Analysis, H. Begeher and A. Jeffrey (eds.), Pitman Res. Notes Math. Ser. 263, Longman, 1992, 15-42.
• [13] R. Nagel (ed.), One-Parameter Semigroups of Positive Operators, Springer, 1986.
• [14] K. Taira, On the existence of Feller semigroups with boundary conditions, II, J. Funct. Anal. 129 (1995), 108-131.
• [15] C. A. Timmermans, On $C_0$-semigroups in a space of bounded continuous functions in the case of entrance or natural boundary points, in: Approximation and Optimization, J. A. Gómez Fernández et al. (eds.), Lecture Notes in Math. 1354, Springer, 1988, 209-216.