Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.For boundary value problems for degenerate-elliptic equations of second order in ⊂ Rn there are cases when a closed surface exists, dividing into two subdomains in such a manner that two new correct boundary value problems can be formulated without introducing new boundary conditions. Such surfaces are called interior boundaries. Some theoretical results regarding the connections between the solutions of the original problem and the two new problems are given. Some numerical experiments using the finite elements method are carried out trying to visualize the effects of the presence of such interior boundary when n = 2. Also some more precise study of the solutions in the case n = 2 is presented

On Principle Eigenvalue for Linear Second Order Elliptic Equations in Divergence Form

2002 Mathematics Subject Classification: 35J15, 35J25, 35B05, 35B50The principle eigenvalue and the maximum principle for second-order elliptic equations is studied. New necessary and sufficient conditions for symmetric and nonsymmetric operators are obtained. Applications for the estimation of the first eigenvalue are given

Global Behavior of the Solutions to Sixth Order Boussinesq Equation with Linear Restoring Force

[Kutev N.; Kutev Nikolai; Кутев Николай]; [Kolkovska N.; Кольковска Н.]; [Dimova M.; Димова М.]Potential well method is established to sixth order Boussinesq equation with linear restoring force and subcritical initial energy. For supercritical initial energy finite time blow up of the solutions is proved under general structural conditions on the initial data. Numerical experiments, illustrating the theoretical results, are presented. 2000 Mathematics Subject Classification: 35L30,76B15,65M06