The study gives a brief overview of publications on exact solutions for functional PDEs with delays of various types and on methods for constructing such solutions. For the first time, second-order wave-type PDEs with a nonlinear source term containi...
This study is devoted to reaction–diffusion equations with spatially anisotropic time delay. Reaction–diffusion PDEs with either constant or variable transfer coefficients are considered. Nonlinear equations of a fairly general form conta...
A family of strongly nonlinear nonstationary equations of mathematical physics with three independent variables is investigated, which contain an arbitrary degree of the first derivative with respect to time and a quadratic combination of second deri...
The paper studies an unsteady equation with quadratic nonlinearity in second derivatives, that occurs in electron magnetohydrodynamics. In mathematics, such PDEs are referred to as parabolic Monge–Ampère equations. An overview of the Mon...
Extreme disasters often induce multiple simultaneous faults in distribution networks, posing significant risks to power supply reliability. Although network reconfiguration and intentional islanding are critical strategies for enhancing system resili...
This paper presents a novel master–slave stochastic optimization framework for the optimal siting and sizing of fixed-step capacitor banks in medium-voltage distribution networks, explicitly addressing the inherent variability of load demand th...