Theory and Applications of Nonlinear Equations with Parameters: Branching, Regularization, Group Symmetry and Solutions Blow-Up
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".
Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 2833
Special Issue Editors
Interests: branching theory of nonlinear equations; bifurcation; singular problems; regularization; approximate methods; differential-operator equations; kinetic systems
Special Issues, Collections and Topics in MDPI journals
Interests: nonlinear partial differential equations; nonlocal differential equations; kinetic equations; Vlasov-Maxwell and Vlasov-Maxwell-Fokker-Planck systems; applications to semiconductors and geophysics
Special Issue Information
Dear Colleagues,
Starting with the seminal works of A.M. Lyapunov, A. Poincaré, and E. Schmidt, the branching theory of nonlinear parameter-dependent equations has enabled various essential applications in natural sciences and engineering over the course of the last hundred years. V.I. Yudovich pioneered the application of symmetry methods in branching theory. A series of applications of the Lyapunov–Schmidt method, Conley index theory, and the central manifold methods in the conditions of group symmetry were reported in many seminal works in recent decades. Various critical processes in plasma physics, fluid dynamics, and thermodynamics are modeled using the branching theory of nonlinear differential-operator parameter-dependent equations. The objective of this Special Issue is to report on the cutting-edge development of the advanced branching theory of nonlinear equations and their applications. The Special issue will bring together experts in the qualitative theory of differential-operator equations, numerical analysts, and practitioners in the various applied fields of contemporary natural sciences. Results on the solvability of non-standard nonlinear equations with parameters will be reported, focusing on the analysis of the problems associated with branching, regularization, group symmetry, and solution blow-up phenomena.
Prof. Dr. Nikolai A. Sidorov
Prof. Dr. Aleksander Sinitsyn
Guest Editors
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