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

[31] The Lambert Function and Exact Solutions of Nonlinear Parabolic Equations
Kosov, A. A.
Semenov, E. I.
RUSSIAN MATHEMATICS, 2019, 63 (08) : 10 - 16
[32] Continuous Dependence of Bounded Φ-Variation Solutions on Parameters for Kurzweil Equations
李宝麟
吴从炘
Northeastern Mathematical Journal, 2005, (04) : 421 - 430
[33] Lipschitz continuous solutions of some doubly nonlinear parabolic equations
Otani, M
Sugiyama, Y
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2002, 8 (03) : 647 - 670
[34] DIFFEOMORPHISMS OF FUNCTION-SPACES CORRESPONDING TO QUASILINEAR PARABOLIC EQUATIONS
KUKSIN, SB
MATHEMATICS OF THE USSR-SBORNIK, 1982, 117 (03): : 359 - 378
[35] CONTINUOUS SOLUTIONS OF SOME OPERATOR EQUATIONS IN ANALYTIC SPACES
NAGNIBID.MI
DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1972, (12): : 1082 - 1085
[36] Existence, stability and smoothness of bounded solutions for an impulsive semilinear system of parabolic equations
Leiva H.
Sivoli Z.
Afrika Matematika, 2018, 29 (7-8) : 1225 - 1235
[37] Absolutely continuous solutions for continuity equations in Hilbert spaces
Da Prato, Giuseppe
Flandoli, Franco
Roeckner, Michael
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2019, 128 : 42 - 86
[38] BOUNDED AND ALMOST PERIODIC-SOLUTIONS OF SEMI-LINEAR PARABOLIC EQUATIONS
WARD, JR
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1988, 18 (02) : 479 - 494
[39] L1 CONTRACTION FOR BOUNDED (NONINTEGRABLE) SOLUTIONS OF DEGENERATE PARABOLIC EQUATIONS
Endal, J.
Jakobsen, E. R.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2014, 46 (06) : 3957 - 3982
[40] Uniqueness and non-uniqueness of bounded solutions to singular nonlinear parabolic equations
Punzo, Fabio
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (08) : 3020 - 3029

← 1 2 3 4 5 →