Abstract In this paper, we study a singular Finsler double phase problem with nonlinear boundary condition and perturbations that have type of critical growth, even on the boundary. Based variational methods in combination truncation techniques, prove existence at least one weak solution for under very general assumptions. Even case when manifold reduces to Euclidean norm, our work is first dea...

Sufficient optimality criteria are derived for a control problem under generalized invexity. A Mond-Weir type dual to the control problem is proposed and various duality theorems are validated under generalized invexity assumptions on functionals appearing in the problems. It is pointed out that these results can be applied to the control problem with free boundary conditions and have linkage w...

This paper deals with a theoretical mathematical analysis of one-dimensional solidification problem, in which kinetic undercooling is incorporated into the This temperature condition at the interface. A model problem with nonlinear kinetic law is considered. We prove a local result intimate for the uniqueness of solution of the corresponding free boundary problem.

Absorbing Boundary Condition for Nonlinear Euler Equations in primitive variables are presented based on the Perfectly Matched Layer (PML) technique. To facilitate the application of PML complex change of variables in the frequency domain, new auxiliary variables are introduced. The final form of the absorbing equations is presented in unsplit physical primitive variables. Both the two-dimensio...

In this paper we propose the analysis of the incompressible nonhomogeneous Navier-Stokes equations with nonlinear outflow boundary condition. This kind of boundary condition appears to be, in some situations, a useful way to perform numerical computations of the solution to the unsteady Navier-Stokes equations when the Dirichlet data are not given explicitly by the physical context on a part of...

A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary condition is analyzed by investigating the energy of the system. Results obtained with this (non...