Eliminating Mixed Asymptotics in Obstacle Type Free Boundary Problems

Multidimensional Transonic Shocks and Free Boundary Problems for Nonlinear Equations of Mixed Type

We are concerned with the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as the following second-order nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential φ : Ω ⊂ R → R: ...

Asymptotics of a Free Boundary Problem

As was shown by Kaper and Kwong Diierential and Integral Equations 3, 353{362], there exists a unique R > 0, such that the diierential equation u 00 + 2 + 1 r u 0 + u ? u q = 0; r > 0; (0 q < 1, 0) admits a classical solution u, which is positive and monotone on (0; R) and which satisses the boundary conditions u 0 (0) = 0; u(R) = u 0 (R) = 0: In this article it is shown that u(0) is bounded, b...

Computation of Mixed Type Functional Differential Boundary Value Problems

Abstract. We study boundary value differential-difference equations where the difference terms may contain both advances and delays. Special attention is paid to connecting orbits, in particular to the modeling of the tails after truncation to a finite interval, and we reformulate these problems as functional differential equations over a bounded domain. Connecting orbits are computed for sever...

Boundary value problems for mixed type equations and applications

Self-similar intermediate asymptotics for nonlinear degenerate parabolic free-boundary problems that occur in image processing.

In the boundary layers around the edges of images, basic nonlinear parabolic equations for image intensity used in image processing assume a special degenerate asymptotic form. An asymptotic self-similar solution to this degenerate equation is obtained in an explicit form. The solution reveals a substantially nonlinear effect-the formation of sharp steps at the edges of the images, leading to e...