Review of Monograph ”Toward General Theory of Differential – Operator and Kinetic Models”

Abstract

The brief review of monograph [Sidorov N., Sidorov D., Sinitsyn A. Toward General Theory of Differential-Operator and Kinetic Models. Book Series: World Scientific Series on Nonlinear Science Series A vol. 97, eds. Prof. L. Chua, World Scientific, Singapore, London, 2020] is provided. This monograph devoted to the state-ofthe-art methods for the non-standard classes of differential operator and kinetic equations from a constructive point of view. In addition to the qualitative problems associated with the proof of existence theorems, bifurcation and blow-up of solutions of nonlinear systems, this monograph provides the formulations of the novel initial-boundary value problems in function spaces. Attention is paid to the problem of constructing asymptotic approximations of solutions and numerical-analytical analysis in mathematical modeling.

Keywords

• mathematical modeling
• nonlinear analysis
• plasma
• vlasov-maxwell equation
• bifurcation
• regularization
• lyapunov-schmidt method