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Abstract Parabolic Evolution Equations and Lojasiewicz-Simon Inequality II - Applications (Paperback, 1st ed. 2021)
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Abstract Parabolic Evolution Equations and Lojasiewicz-Simon Inequality II - Applications (Paperback, 1st ed. 2021)
Series: SpringerBriefs in Mathematics
Expected to ship within 10 - 15 working days
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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 Lojasiewicz-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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