Bounded solutions of parabolic equations in continuous function spaces

被引：7

作者：

Liu, James ^{[1
]}

N'Guerekata, Gaston ^{[2
]}

Van Minh, Nguyen ^{[3
]}

Phong, Vu Quoc ^{[4
]}

机构：

[1] James Madison Univ, Dept Math, Harrisonburg, VA 22807 USA

[2] Morehead State Univ, Dept Math, Baltimore, MD 21251 USA

[3] Univ W Georgia, Dept Math, Carrollton, GA 30118 USA

[4] Ohio Univ, Dept Math, Athens, OH 45701 USA

来源：

FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA | 2006年 / 49卷 / 03期

关键词：

parabolic equation; continuous function space; complete second order evolution equation; mild solution;

D O I：

10.1619/fesi.49.337

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the existence of bounded mild solutions to equations of the form u(1)(t) = Au(t) + f(t), where A generates a holomorphic semigroup that is not necessarily strongly continuous, and f is a bounded function. This problem arises when one considers a parabolic equation in spaces of continuous functions. The obtained results, that are stated in terms of spectral properties of the spectrum of A and the uniform spectrum of f, extend previous ones.

引用

页码：337 / 355

页数：19

共 50 条

[1] BOUNDED SOLUTIONS OF NONLINEAR PARABOLIC EQUATIONS
Mavinga, Nsoki
Nkashama, Mubenga N.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, : 207 - 220
[2] EXISTENCE OF BOUNDED SOLUTIONS OF SOME NONLINEAR PARABOLIC EQUATIONS
MOKRANE, A
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1987, 107 : 313 - 326
[3] Existence and stability of bounded solutions for a system of parabolic equations
Leiva, H
Sequera, I
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 279 (02) : 495 - 507
[4] On Bounded Solutions for Nonlinear Parabolic Equations with Degenerate Coercivity
Ahmed Youssfi
Abdelmoujib Benkirane
Youssef El Hadfi
Mediterranean Journal of Mathematics, 2016, 13 : 3029 - 3040
[5] Bounded solutions for non-autonomous parabolic equations
Zhang, WN
Stewart, I
DYNAMICS AND STABILITY OF SYSTEMS, 1996, 11 (02): : 109 - 120
[6] BOUNDED SOLUTIONS OF LINEAR PERIODIC ABSTRACT PARABOLIC EQUATIONS
LUNARDI, A
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1988, 110 : 135 - 159
[7] On Bounded Solutions for Nonlinear Parabolic Equations with Degenerate Coercivity
Youssfi, Ahmed
Benkirane, Abdelmoujib
El Hadfi, Youssef
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2016, 13 (05) : 3029 - 3040
[8] BOUNDED SOLUTIONS OF PARABOLIC EQUATIONS IN UNBOUNDED-DOMAINS
SCARPELLINI, B
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 22 (05) : 625 - 647
[9] Parabolic differential equations in ordered Banach spaces of bounded functions
Grenon, N
Moutoussamy, I
Simon, A
Volkmann, P
POSITIVITY, 1997, 1 (01) : 45 - 54
[10] Parabolic Differential Equations in Ordered Banach Spaces of Bounded Functions
Nathalie Grenon
Isabelle Moutoussamy
Alice Simon
Peter Volkmann
Positivity, 1997, 1 : 45 - 54

← 1 2 3 4 5 →