Fractional-in-Time Semilinear Parabolic Equations and Applications
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Beschreibung
This book provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to certain fractional kinetic equations. This class of equations is characterized by the presence of a nonlinear time-dependent source, generally of arbitrary growth in the unknown function, a time derivative in the sense of Caputo and the presence of a large class of diffusion operators. The global regularity problem is then treated separately and the analysis is extended to some systems of fractional kinetic equations, including prey-predator models of Volterra–Lotka type and chemical reactions models, all of them possibly containing some fractional kinetics.
Besides classical examples involving the Laplace operator, subject to standard (namely, Dirichlet, Neumann, Robin, dynamic/Wentzell and Steklov) boundary conditions, the framework also includes non-standard diffusion operators of "fractional" type, subject to appropriate boundary conditions.This book is aimed at graduate students and researchers in mathematics, physics, mathematical engineering and mathematical biology whose research involves partial differential equations.
This book provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to certain fractional kinetic equations. This class of equations is characterized by the presence of a nonlinear time-dependent source, generally of arbitrary growth in the unknown function, a time derivative in the sense of Caputo and the presence of a large class of diffusion operators. The global regularity problem is then treated separately and the analysis is extended to some systems of fractional kinetic equations, including prey-predator models of Volterra–Lotka type and chemical reactions models, all of them possibly containing some fractional kinetics.
Besides classical examples involving the Laplace operator, subject to standard (namely, Dirichlet, Neumann, Robin, dynamic/Wentzell and Steklov) boundary conditions, the framework also includes non-standard diffusion operators of "fractional" type, subject to appropriate boundary conditions.
This book is aimed at graduate students and researchers in mathematics, physics, mathematical engineering and mathematical biology, whose research involves partial differential equations.
Provides a general framework which will facilitate the further study of nonlocal reaction-diffusion systems Addresses the existence of (non-regular) mild solutions, strong solutions, and the global regularity problem Establishes clear connections between fractional in time and classical parabolic problems
Autor*in
Ciprian G. Gal
Themen in »Fractional-in-Time Semilinear Parabolic Equations and Applications«
Semilinear parabolic equations Caputo fractional derivative Anomalous diffusion Fractional Laplace operator Existence and regularity of solutions Reaction-diffusion systems Fractional in time equations Fractional Brownian motion Lévy flight Schneider-Grey Brownian motion partial differential equations