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Mathematical and Numerical Analysis of Nonlinear Evolution Equations

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 t...

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Format: Online
Sprog:engelsk
Udgivet: MDPI - Multidisciplinary Digital Publishing Institute 2021
Fag:
boundedness
delay
Hopf bifurcation
Lyapunov functional
stability
SEIQRS-V model
kinetic theory
integro-differential equations
complex systems
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
active particles
autoimmune disease
degenerate equations
real activity variable
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
thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general
thema EDItEUR::P Mathematics and Science
Online adgang:ONIX_20210501_9783039432721_906
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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.

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