TY - BOOK ID - 137007524 TI - Mathematical and Numerical Analysis of Nonlinear Evolution Equations : Advances and Perspectives PY - 2020 PB - Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute DB - UniCat KW - boundedness KW - delay KW - Hopf bifurcation KW - Lyapunov functional KW - stability KW - SEIQRS-V model KW - kinetic theory KW - integro-differential equations KW - complex systems KW - evolution equations KW - thermostat KW - nonequilibrium stationary states KW - discrete Fourier transform KW - discrete kinetic theory KW - nonlinearity KW - fractional operators KW - Cahn–Hilliard systems KW - well-posedness KW - regularity KW - optimal control KW - necessary optimality conditions KW - Schrödinger equation KW - Davydov’s model KW - partial differential equations KW - exact solutions KW - fractional derivative KW - abstract Cauchy problem KW - C0−semigroup KW - inverse problem KW - active particles KW - autoimmune disease KW - degenerate equations KW - real activity variable KW - Cauchy problem KW - electric circuit equations KW - wardoski contraction KW - almost (s, q)—Jaggi-type KW - b—metric-like spaces KW - second-order differential equations KW - dynamical systems KW - compartment model KW - epidemics KW - basic reproduction number UR - https://www.unicat.be/uniCat?func=search&query=sysid:137007524 AB - 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. ER -