Global existence, uniqueness, and continuous dependence for a semilinear initial value problem

Journal of Mathematical Analysis and Applications

Volumn 280, Issue 2, 2003, Pages 413-423

  Periago, Francisco ^a  

^a TECHNICAL UNIVERSITY OF CARTAGENA   (Spain)

Author keywords

Continuous dependence; Global existence; Semilinear initial value problem; Uniqueness

Indexed keywords

EID: 0038392430     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(03)00126-4     Document Type: Article

References (12)

1. T. Cazenave, A. Haraux, An Introduction to Semilinear Evolution Equations, in: Oxford Lecture Series in Mathematics and Its Applications, Vol. 13, 1998.
2. G. Da Prato, E. Sinestrari, Differential operators with non dense domain, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 (1987) 285-344.
3. J. Dieudonné, Foundations of Modern Analysis, Academic Press, New York, 1969.
4. H. Kielhöfer, Existenz und Regularität von Lösungen semilinearer parabolischer Anfangs-Randwertprobleme, Math. Z. 142 (1975) 131-160.
5. A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel, 1995.
6. C. Martinez, M. Sanz, The Theory of Fractional Powers of Operators, in: North-Holland Mathematics Studies, Vol. 187, Elsevier, 2001.
7. I. Miyadera, S. Oharu, N. Okazawa, Generation theorems of semi-groups of linear operators, Publ. Res. Inst. Math. Sci. 8 (1972/1973) 509-555.
8. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
9. F. Periago, B. Straub, A functional calculus for almost sectorial operators and applications to abstract evolution equations, J. Evol. Equations 2 (2002) 41-68.
10. I. Podlubny, Fractional Differential Equations, Academic Press, 1999.
11. J.M.A.M. van Neerven, B. Straub, On the existence and growth of mild solutions of the abstract Cauchy problem for operators with polynomially bounded resolvent, Houston J. Math. 24 (1998) 137-171.
12. W. von Wahl, Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen hölderstetiger Funktionen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. 11 (1972) 231-258.