On a reaction–diffusion–advection system: fixed boundary or free boundary

On the Regularity of a Free Boundary Near Contact Points With a Fixed Boundary

We investigate the regularity of a free boundary near contact points with a fixed boundary, with C boundary data, for an obstacle-like free boundary problem. We will show that under certain assumptions on the solution, and the boundary function, the free boundary is uniformly C up to the fixed boundary. We will also construct some examples of irregular free boundaries.

Free-Free, Fixed or Other Test Boundary Conditions for the Best Modal Test?

Deciding on the configuration in which to test a structure is an important consideration which needs to be addressed before a test is carried out. Since the evolution of the modal test, there are several test configurations free-free, fixed, added-mass, amongst othersthat have been developed and used. However, the free-free test configuration remains the most favoured for most applications sinc...

Regularity Properties of a Free Boundary near Contact Points with the Fixed Boundary

In the upper half of the unit ball B = {|x | < 1, x1 > 0}, let u and  (a domain in R+ = {x ∈ R n : x1 > 0} ) solve the following overdetermined problem: 1u = χ in B , u = |∇u| = 0 in B \, u = 0 on 5 ∩ B, where B is the unit ball with center at the origin, χ denotes the characteristic function of , 5 = {x1 = 0}, n ≥ 2, and the equation is satisfied in the sense of distributions. We show (am...

On Free Boundary Problems

On a Two-point Free Boundary Problem

We study a two-point free boundary problem for a quasilinear parabolic equation. This problem arises in the model of flame propagation in combustion theory. It also arises in the study of the motion of interface moving with curvature in which the studied problem is confined in the conical region bounded by two straight lines and the interface has prescribed touching angles with these two straig...