[1] Wang Jing, Xue Xingmei,. Existence results for a class of parabolic evolution equationsin Banach spaces [J]. Journal of Southeast University (English Edition), 2003, 19 (2): 182-187. [doi:10.3969/j.issn.1003-7985.2003.02.018]
Copy
Existence results for a class of parabolic evolution equationsin Banach spaces(
)
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 19
- Issue:
- 2003 2
- Page:
- 182-187
- Research Field:
- Mathematics, Physics, Mechanics
- Publishing date:
- 2003-06-30
Info
- Title:
- Existence results for a class of parabolic evolution equationsin Banach spaces
- Author(s):
- Wang Jing; Xue Xingmei
- Department of Mathematics, Southeast University, Nanjing 210096, China
- Keywords:
- evolution system; analytic semigroup; mild solution; semi-classical solution; classical solution
- PACS:
- O177.2
- DOI:
- 10.3969/j.issn.1003-7985.2003.02.018
- Abstract:
- We discuss the existence results of the parabolic evolution equation d(x(t)+g(t, x(t)))/dt+A(t)x(t)=f(t, x(t)) in Banach spaces, where A(t) generates an evolution system and functions f, g are continuous. We get the theorem of existence of a mild solution, the theorem of existence and uniqueness of a mild solution and the theorem of existence and uniqueness of an S-classical(semi-classical)solution. We extend the cases when g(t)=0 or A(t)=A.
References:
[1] Pazy A. Semigroups of linear operators and applications to partial differential equations[M]. New York: Springer-Verlag, 1983.
[2] Goldstein Jerome A. Semigroups of linear operators and applications[M]. New York: The Clarendon Press, Oxford University Press, 1985.
[3] Eduardo Hernández M. Existence results for a class of semi-linear evolution equations[J]. Electronic Journal of Differential Equations, 2001(24):1-14.
[4] Eduardo Hernández, Henri′quez Hernán R. Existence of periodic solutions of partial neutral functional-differential equations with unbounded delay[J]. J Math Anal Appl, 1998, 221(2):499-522.
[5] Eduardo Hernández, Henri′quez Hernán R. Existence results for partial neutral functional-differential equations with unbounded delay[J]. J Math Anal Appl, 1998, 221(2): 452-475.
[6] Hale J. Functional differential equations[M]. New York: Springer-Verlag, 1971.
[7] Fitzgibbon W E. Semilinear functional differential equations in Banach space[J]. Journal of Differential Equations, 1978, 29:1-14.
[8] Friedman A. Partial differential equations[M]. New York:Holt, Rinehart and Winston Press, 1969.
Memo
- Memo:
- Biographies: Wang Jing(1976—), female, graduate; Xue Xingmei(corresponding author), male, doctor, associate professor, xmxue@seu.edu.cn.