Impulsive nonlocal nonlinear parabolic differential problems.
Instability of mixed finite elements for Richards' equation
Richards' equation is a widely used model of partially saturated flow in a porous medium. In order to obtain conservative velocity field several authors proposed to use mixed or mixed-hybrid schemes to solve the equation. In this paper, we shall analyze the mixed scheme on 1D domain and we show that it violates the discrete maximum principle which leads to catastrophic oscillations in the solution.
Invariant Rectangles and Strongly Coupled Semilinear Parabolic.
Invariant regions associated with quasilinear damped wave equations
Invariant wedges for a two-point reflecting Brownian motion and the “hot spots” problem.