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

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