A Posteriori Error Estimates in H1 (W) Spaces for Parabolic Quasi-Variational Inequalities with Linear Source Terms Related to American Options Problem

Existence of Positive Weak Solutions for Quasi-Linear Kirchhoff Elliptic Systems via Sub-Supersolutions Concept

“…Studying these equations is a daunting task because there are no general methods for solving them. Each problem requires an appropriate approach depending on the type of linearity ( [1][2][3][4][5][6][7][8][9][10]).…”

A posteriori error estimates for the generalized Schwarz method of a new class of advection‐diffusion equation with mixed boundary condition

“…Then a result of asymptotic behavior in Sobolev norm has been given. The same study has been conducted in the evolutionary free boundary problems in Boulaaras, Allahem et al, and Boulaaras et al …”

“…Herman Amandus Schwarz created it in 1890. Scientists have used this method to resolve stationary or evolutionary boundary value problems on domains that consist of 2 or more overlapping subdomains (see previous studies [2][3][4][5][6][7][8][9][10] and other works 1,[11][12][13][14][15][16][17][18][19][20]. The resolution of these problems is approximated by an infinite sequence of functions derived from the solution of a sequence of elliptic or parabolic boundary value problems in each of the subdomains.…”

“…Then a result of asymptotic behavior in Sobolev norm has been given. The same study has been conducted in the evolutionary free boundary problems in Boulaaras, 10 Allahem et al, 6 and Boulaaras et al 7 To complete the previous works, we apply in this paper the same study for the hyperbolic equations, which is a very active area of research. The main distinguishing feature of the initial boundary value problems is the fact that perturbations propagate with finite speed.…”