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Free Boundary Problem of Magnetohydrodynamics

Journal of Mathematical Sciences, 2015
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E. Frolova
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A qualitative analysis of a free boundary problem modeling tumor growth with angiogenesis

Nonlinear Analysis: Real World Applications, 2019
In this paper we consider a free boundary problem modeling tumor growth with angiogenesis. The model is a free boundary problem of a system of partial differential equations.
Xuemei Wei
exaly   +2 more sources

On a Free Boundary Problem

Mathematical Methods in the Applied Sciences, 1996
Summary: This paper considers a discontinuous semilinear elliptic problem: \[ - \Delta u= g(u)H(u-\mu) \quad \text{in } \Omega, \qquad u=h \text{ on } \partial \Omega, \] where \(H\) is the Heaviside function, \(\mu\) a real parameter and \(\Omega\) the unit ball in \(\mathbb{R}^2\). We deal with the existence of solutions under suitable conditions on \
Boucherif, Abdelkader   +1 more
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Ill-Posedness of Free Boundary Problem of the Incompressible Ideal MHD

Communications in Mathematical Physics, 2018
In the present paper, we show the ill-posedness of the free boundary problem of the incompressible ideal magnetohydrodynamics (MHD) equations in two spatial dimensions for any positive vacuum permeability $$\mu _0$$ μ 0 , in Sobolev spaces.
Chengchun Hao, T. Luo
semanticscholar   +1 more source

Free Boundary Problem

SIAM Journal on Mathematical Analysis, 1974
Let $\mathcal{D}$ be a doubly connected region in the complex plane limited by the infinite point and a convex set $\Gamma $. If $\lambda > 0$, then we study the existence, uniqueness and geometry of annuli $\omega \subset \mathcal{D}$ having $\Gamma $ as one boundary component and another boundary component $\gamma $, such that there exists a harmonic
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