The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

The two-level penalty finite element methods for Navier-Stokes equations with nonlinear slip boundary conditions are investigated in this paper, whose variational formulation is the Navier-Stokes type variational inequality problem of the second kind. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size H in combining with solving a St...

In this paper, the concept of pseudoconvexity and quasiconvexity for continuous~-time functions are studied and an equivalence condition for pseudoconvexity is obtained. Moreover, under pseudoconvexity assumptions, some relationships between Minty and Stampacchia vector variational inequalities and continuous-time programming problems are presented. Finally, some characterizations of the soluti...

We will discuss the so-called mixed endpoint conditions for variational problems with non-holonomic constraints given by form actions of order greater than one. We will present some results and discuss the inverse problem of Calculus of Variations.

Based on the very recent work by Censor-Gibali-Reich [7], we propose an extension of their new variational problem (Split Variational Inequality Problem) to monotone variational inclusions. Relying on the Krasnoselskii-Mann Theorem for averaged operators, we analyze an algorithm for solving a new split monotone inclusions under weaker conditions. Our results improve and develop previously discu...