We study the large time behaviour of solution linear dispersive partial differential equations posed on a finite interval, when at least one prescribed boundary conditions is periodic. use Q equation approach, pioneered in Fokas & Lenells 2012 and applied to problems half-line van der Weele 2021, characterise necessary for such problem be periodic, an asymptotic sense. then fully describe perio...

Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The method of lines (M...

In this short note, we want to describe the logarithmic convexity argument for third order in time partial differential equations. As a consequence, first prove uniqueness result whenever certain conditions on parameters are satisfied. Later, show instability of solutions if initial energy is less or equal than zero.

In this paper we derive a fourth-order nonlinear partial differential equation modelling the effects of suction/blowing on the evolution of the free surface of a thin viscous film on a porous base. Gravity and surface tension effects are included. The suction/blowing is modelled as an arbitrary function vn(t, r). The Lie group classification method is used to determine a firstorder quasi-linear...