Well-posedness of Third Order Differential Equations in Hölder Continuous Function Spaces

In this paper, by using operator-valued ${\dot{C}}^{\unicode[STIX]{x1D6FC}}$ -Fourier multiplier results on vector-valued Hölder continuous function spaces, we give a characterization of the $C^{\unicode[STIX]{x1D6FC}}$ -well-posedness for the third order differential equations $au^{\prime \prime \p...

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Veröffentlicht in:Canadian mathematical bulletin Jg. 62; H. 4; S. 715 - 726
Hauptverfasser: Bu, Shangquan, Cai, Gang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Canada Canadian Mathematical Society 01.12.2019
Cambridge University Press
Schlagworte:
Banach spaces
Continuity (mathematics)
Differential equations
Function space
Linear operators
Mathematical analysis
Operators (mathematics)
Well posed problems
34K30
47D06
34G10
Ċ -Fourier multiplier
degenerate differential equation
47A10
C -well-posedness
Hölder continuous function space
ISSN:0008-4395, 1496-4287
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Zusammenfassung:In this paper, by using operator-valued ${\dot{C}}^{\unicode[STIX]{x1D6FC}}$ -Fourier multiplier results on vector-valued Hölder continuous function spaces, we give a characterization of the $C^{\unicode[STIX]{x1D6FC}}$ -well-posedness for the third order differential equations $au^{\prime \prime \prime }(t)+u^{\prime \prime }(t)=Au(t)+Bu^{\prime }(t)+f(t)$ , ( $t\in \mathbb{R}$ ), where $A,B$ are closed linear operators on a Banach space $X$ such that $D(A)\subset D(B)$ , $a\in \mathbb{C}$ and $0<\unicode[STIX]{x1D6FC}<1$ .
Bibliographie:ObjectType-Article-1
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ISSN:0008-4395
1496-4287
DOI:10.4153/S0008439518000048