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Abstract Parabolic Evolution Equations and Lojasiewicz–Simon Inequality II
Af: Atsushi Yagi Engelsk Paperback
SPAR
kr 134
Abstract Parabolic Evolution Equations and Lojasiewicz–Simon Inequality II
Af: Atsushi Yagi Engelsk Paperback
This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz-Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described.

Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller-Segel equations in one-, two-, and three-dimensional spaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more.

Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed.
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This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz-Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described.

Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller-Segel equations in one-, two-, and three-dimensional spaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more.

Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed.
Produktdetaljer
Sprog: Engelsk
Sider: 128
ISBN-13: 9789811626623
Indbinding: Paperback
Udgave:
ISBN-10: 9811626626
Udg. Dato: 13 aug 2021
Længde: 0mm
Bredde: 235mm
Højde: 155mm
Oplagsdato: 13 aug 2021
Forfatter(e): Atsushi Yagi
Forfatter(e) Atsushi Yagi


Kategori Funktionsanalyse og transformation


Sprog Engelsk


Indbinding Paperback


Sider 128


Udgave


Længde 0mm


Bredde 235mm


Højde 155mm


Udg. Dato 13 aug 2021


Oplagsdato 13 aug 2021

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