Overview
- 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
Part of the book series: Mathématiques et Applications (MATHAPPLIC, volume 84)
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Table of contents (5 chapters)
Keywords
- 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
About this book
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.
Authors and Affiliations
About the authors
Mahamadi Warma is Professor at George Mason University in Fairfax, Virginia (USA). His reseach focuses on linear and nonlinear partial differential equations, fractional PDEs and their controllability-observability properties.
Bibliographic Information
Book Title: Fractional-in-Time Semilinear Parabolic Equations and Applications
Authors: Ciprian G. Gal, Mahamadi Warma
Series Title: Mathématiques et Applications
DOI: https://doi.org/10.1007/978-3-030-45043-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-45042-7Published: 24 September 2020
eBook ISBN: 978-3-030-45043-4Published: 23 September 2020
Series ISSN: 1154-483X
Series E-ISSN: 2198-3275
Edition Number: 1
Number of Pages: XII, 184
Number of Illustrations: 103 b/w illustrations
Topics: Partial Differential Equations, Applications of Mathematics, Mathematical Methods in Physics