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Evolution Equations in Scales of Banach Spaces
(Englisch)
Teubner-Texte zur Mathematik 140
Oliver Caps

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Evolution Equations in Scales of Banach Spaces

Produktbeschreibung

Zusammenstellung aktueller Forschungsergebnisse
Dr. Oliver Caps, Universität Mainz
Tools from functional analysis - Well-posedness of the time-dependent linear Cauchy problem - Quasilinear evolution equations - Applications to linear, time-dependent evolution equations - Applications to quasilinear evolution equations
The book provides a new functional-analytic approach to evolution equations by considering the abstract Cauchy problem in a scale of Banach spaces. Conditions are proved characterizing well-posedness of the linear, time-dependent Cauchy problem in scales of Banach spaces and implying local existence, uniqueness, and regularity of solutions of the quasilinear Cauchy problem. Many applications illustrate the generality of the approach. In particular, using the Fefferman-Phong inequality unifying results on parabolic and hyperbolic equations generalizing classical ones and a unified treatment of Navier-Stokes and Euler equations is described. Assuming only basic knowledge in analysis and functional analysis the book provides all mathematical tools and is aimed for students, graduates, researchers, and lecturers.
Neuer funktional-analytischer Zugang
The book provides a new functional-analytic approach to evolution equations by considering the abstract Cauchy problem in a scale of Banach spaces. Conditions are proved characterizing well-posedness of the linear, time-dependent Cauchy problem in scales of Banach spaces and implying local existence, uniqueness, and regularity of solutions of the quasilinear Cauchy problem.
From the content:

Tools from functional analysis - Well-posedness of the time-dependent linear Cauchy problem - Quasilinear evolution equations - Applications to linear, time-dependent evolution equations - Applications to quasilinear evolution equations
Dr. Oliver Caps, Universität Mainz

Über den Autor



Dr. Oliver Caps, Universität Mainz


Inhaltsverzeichnis



Tools from functional analysis - Well-posedness of the time-dependent linear Cauchy problem - Quasilinear evolution equations - Applications to linear, time-dependent evolution equations - Applications to quasilinear evolution equations


Klappentext



The book provides a new functional-analytic approach to evolution equations by considering the abstract Cauchy problem in a scale of Banach spaces. Conditions are proved characterizing well-posedness of the linear, time-dependent Cauchy problem in scales of Banach spaces and implying local existence, uniqueness, and regularity of solutions of the quasilinear Cauchy problem. Many applications illustrate the generality of the approach. In particular, using the Fefferman-Phong inequality unifying results on parabolic and hyperbolic equations generalizing classical ones and a unified treatment of Navier-Stokes and Euler equations is described. Assuming only basic knowledge in analysis and functional analysis the book provides all mathematical tools and is aimed for students, graduates, researchers, and lecturers.




The book provides a new functional-analytic approach to evolution equations by considering the abstract Cauchy problem in a scale of Banach spaces. Conditions are proved characterizing well-posedness of the linear, time-dependent Cauchy problem in scales of Banach spaces and implying local existence, uniqueness, and regularity of solutions of the quasilinear Cauchy problem.


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