Reprint
Mathematical and Numerical Analysis of Nonlinear Evolution Equations
Advances and Perspectives
Edited by
October 2020
208 pages
- ISBN978-3-03943-272-1 (Hardback)
- ISBN978-3-03943-273-8 (PDF)
This book is a reprint of the Special Issue Mathematical and Numerical Analysis of Nonlinear Evolution Equations : Advances and Perspectives that was published in
Computer Science & Mathematics
Engineering
Physical Sciences
Public Health & Healthcare
Summary
The topic of this book is the mathematical and numerical analysis of some recent frameworks based on differential equations and their application in the mathematical modeling of complex systems, especially of living matter. First, the recent new mathematical frameworks based on generalized kinetic theory, fractional calculus, inverse theory, Schrödinger equation, and Cahn–Hilliard systems are presented and mathematically analyzed. Specifically, the well-posedness of the related Cauchy problems is investigated, stability analysis is also performed (including the possibility to have Hopf bifurcations), and some optimal control problems are presented. Second, this book is concerned with the derivation of specific models within the previous mentioned frameworks and for complex systems in biology, epidemics, and engineering. This book is addressed to graduate students and applied mathematics researchers involved in the mathematical modeling of complex systems.
Format
- Hardback
License
© 2020 by the authors; CC BY-NC-ND license
Keywords
boundedness; delay; Hopf bifurcation; Lyapunov functional; stability; SEIQRS-V model; kinetic theory; integro-differential equations; complex systems; stability; evolution equations; thermostat; nonequilibrium stationary states; discrete Fourier transform; discrete kinetic theory; nonlinearity; fractional operators; Cahn–Hilliard systems; well-posedness; regularity; optimal control; necessary optimality conditions; Schrödinger equation; Davydov’s model; partial differential equations; exact solutions; fractional derivative; abstract Cauchy problem; C0−semigroup; inverse problem; kinetic theory; active particles; autoimmune disease; fractional derivative; abstract Cauchy problem; evolution equations; degenerate equations; real activity variable; thermostat; nonlinearity; complex systems; Cauchy problem; electric circuit equations; wardoski contraction; almost (s, q)—Jaggi-type; b—metric-like spaces; second-order differential equations; dynamical systems; compartment model; epidemics; basic reproduction number; stability