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Mathematical and Numerical Analysis of Nonlinear Evolution Equations
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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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Keywords
- abstract Cauchy problem
- active particles
- almost (s, q)—Jaggi-type
- autoimmune disease
- basic reproduction number
- boundedness
- b—metric-like spaces
- C0−semigroup
- Cahn–Hilliard systems
- Cauchy problem
- compartment model
- complex systems
- Davydov’s model
- degenerate equations
- Delay
- discrete Fourier Transform
- discrete kinetic theory
- dynamical systems
- electric circuit equations
- Epidemics
- evolution equations
- exact solutions
- fractional derivative
- fractional operators
- Hopf bifurcation
- Integro-differential equations
- inverse problem
- kinetic theory
- Lyapunov functional
- Mathematics & science
- necessary optimality conditions
- nonequilibrium stationary states
- nonlinearity
- Optimal Control
- Partial Differential equations
- real activity variable
- Reference, information & interdisciplinary subjects
- regularity
- Research & information: general
- Schrödinger equation
- second-order differential equations
- SEIQRS-V model
- Stability
- thermostat
- wardoski contraction
- well-posedness
Links
DOI: 10.3390/books978-3-03943-273-8Editions