Vector F-implicit complementarity problems in Banach spaces

AbstractIn this work, a new class of vector F-implicit complementarity problems and vector F-implicit variational inequality problems are introduced and studied, and the equivalence between of them is presented under certain assumptions in Banach spaces. We also derive some new existence theorems of solutions for the vector F-implicit complementarity problems and the vector F-implicit variational inequality problems by using the FKKM theorem under some suitable assumptions without monotonicity

On the generalized vector F-implicit complementarity problems and vector F-implicit variational inequality problems

In this paper, we introduce and analyze some new classes of generalized vector-F implicit complementarity problems and the general mixed vector-F variational inequalities. Under suitable conditions, we prove the equivalences between these new problems. We establish several existence theorems for these classes of vector-F complementarity and general mixed vector-F variational inequalities using a new version of the Fan-KKM theorem in Hausdorff topological vector spaces, and without even using the classical assumptions in this context, like monotonicity or continuity. Results obtained in this paper represent significant improvement and refinement of the previously known results

Signorini conditions for inviscid fluids

In this thesis, we present a new type of boundary condition for the simulation of inviscid fluids – the Signorini boundary condition. The new condition models the non-sticky contact of a fluid with other fluids or solids. Euler equations with Signorini boundary conditions are analyzed using variational inequalities. We derived the weak form of the PDEs, as well as an equivalent optimization based formulation. We proposed a finite element method to numerically solve the Signorini problems. Our method is based on a staggered grid and a level set representation of the fluid surfaces, which may be plugged into an existing fluid solver. We implemented our algorithm and tested it with some 2D fluid simulations. Our results show that the Signorini boundary cpndition successfully models some interesting contact behavior of fluids, such as the hydrophobic contact and the non-coalescence phenomenon

Vector F-implicit complementarity problems in topological vector spaces

AbstractRecently, Huang and Li [J. Li, N.J. Huang, Vector F-implicit complementarity problems in Banach spaces, Appl. Math. Lett. 19 (2006) 464–471] introduced and studied a new class of vector F-implicit complementarity problems and vector F-implicit variational inequality problems in Banach spaces. In this work, we study this class in topological vector spaces and drive some existence theorems for the vector F-implicit variational inequality and vector F-implicit complementarity problem. Also, their equivalence is presented under certain conditions