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

被引：12

作者：

Periago, F ^{[1
]}

机构：

[1] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Cartagena 30203, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2003年 / 280卷 / 02期

关键词：

global existence; uniqueness; continuous dependence; semilinear initial value problem;

D O I：

10.1016/S0022-247X(03)00126-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the semilinear initial value problem associated with an operator A whose spectrum lies in a sector of the complex plane and whose resolvent satisfies parallel to(z - A)-1parallel to less than or equal to M\z\(gamma) for some -1 < gamma < 0 and all z outside the sector. The properties of existence and uniqueness of global mild solutions and continuous dependence on the initial data are investigated. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：413 / 423

页数：11

共 12 条

[1] Cazenave T., 1998, An Introduction to Semilinear Evolution Equations
[2] Dieudonne J., 1969, Foundations of Modern Analysis
[3] EXISTENCE AND REGULARITY OF SOLUTIONS OF SEMILINEAR PARABOLIC INITIAL - BOUNDARY-VALUE PROBLEMS
KIELHOFER, H
[J]. MATHEMATISCHE ZEITSCHRIFT, 1975, 142 (02) : 131 - 160
[4] Lunardi A., 1995, ANAL SEMIGROUPS OPTI
[5] Martinez C., 2001, North-Holland Math. Stud., V187
[6] Miyadera I., 1972, PUBL RES I MATH SCI, V8, P509, DOI DOI 10.2977/PRIMS/1195192960
[7] Pazy A., 1983, SEMIGROUPS LINEAR OP, DOI [10.1007/978-1-4612-5561-1, DOI 10.1007/978-1-4612-5561-1]
[8] A functional calculus for almost sectorial operators and applications to abstract evolution equations
Periago, F
Straub, B
[J]. JOURNAL OF EVOLUTION EQUATIONS, 2002, 2 (01) : 41 - 68
[9] Podlubny I, 1998, Fractional Di ff erential Equations
[10] Prato GD, 1987, Ann. Sc. Pisa Cl. Sci., V14, P285

← 1 2 →