Mathematical and Numerical Analysis of Nonlinear Evolution Equations  Advances and Perspectives 

 - Basel, Switzerland  MDPI - Multidisciplinary Digital Publishing Institute  2020 
 - 1 online resource (208 p.) 
<br/><br/> Open Access 
<br/><br/> 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. 
<br/><br/><br/>Creative Commons 
<br/><br/><br/>English 
<br/><br/><label>ISBN: </label>9783039432721 9783039432738 books978-3-03943-273-8 
<br/><br/><label>Standard No.: </label>10.3390/books978-3-03943-273-8  doi 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Mathematics & science<br/>Research & information: general
<br/><br/><label>Subjects--Index Terms: </label>abstract Cauchy problem active particles almost (s, q)-Jaggi-type autoimmune disease b-metric-like spaces basic reproduction number boundedness 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 necessary optimality conditions nonequilibrium stationary states nonlinearity optimal control partial differential equations real activity variable regularity Schrödinger equation second-order differential equations SEIQRS-V model stability thermostat wardoski contraction well-posedness