Free boundary problem for quasilinear parabolic equation with fixed angle of contact to a boundary

Nvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition

Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...

A two-phase free boundary problem for a semilinear elliptic equation

In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary‎. ‎We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...

A Parabolic Free Boundary Problem with Bernoulli Type Condition on the Free Boundary

Consider the parabolic free boundary problem ∆u− ∂tu = 0 in {u > 0} , |∇u| = 1 on ∂{u > 0} . For a realistic class of solutions, containing for example all limits of the singular perturbation problem ∆uε − ∂tuε = βε(uε) as ε → 0, we prove that one-sided flatness of the free boundary implies regularity. In particular, we show that the topological free boundary ∂{u > 0} can be decomposed into an ...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Blow-up Behavior for a Quasilinear Parabolic Equation with Nonlinear Boundary Condition

In this paper, we study the solution of an initial boundary value problem for a quasilinear parabolic equation with a nonlinear boundary condition. We first show that any positive solution blows up in finite time. For a monotone solution, we have either the single blow-up point on the boundary, or blow-up on the whole domain, depending on the parameter range. Then, in the single blow-up point c...