This paper provides a number of working tools for the discussion of fully nonlinear parabolic equations. These include: a full proof that the maximum principle which provides L∞ estimates of "strong" ...

We study the heat kernel and the Green’s function on the infinite supercritical percolation cluster in dimension d ≥ 2 and prove a quantitative homogenization theorem for these functions with an ...

Off-axis paraboloid reflector is a special optical element, its main function is to focus the incident light to a certain distance from the optical axis. The working principle is based on the ...

Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical ...

Control theory for degenerate parabolic and wave equations has emerged as a vibrant field that combines deep theoretical insights with practical applications across physics and engineering. Such ...