Mean curvature flow with free boundary – Type 2 singularities
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DOI: 10.1002/mana.201800156
Abstract: In this paper we give sufficient conditions that guarantee the mean curvature flow with free boundary on a pinched cylinder develops a Type 2 curvature singularity. We additionally prove that Type 0 singularities may only… read more here.
Keywords: mean curvature; free boundary; type singularities; curvature flow ... See more keywords
On a two‐phase Stefan problem with convective boundary condition including a density jump at the free boundary
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6152
Abstract: We consider a two‐phase Stefan problem for a semi‐infinite body x>0, with a convective boundary condition including a density jump at the free boundary with a time‐dependent heat transfer coefficient of the type h/t ,… read more here.
Keywords: density; free boundary; boundary condition; problem ... See more keywords
On the first bifurcation point for a free boundary problem modeling a small arterial plaque
Sign Up to like & getrecommendations! Published in 2022 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.8087
Abstract: Atherosclerosis occurs when plaque clogs the arteries. It is a leading cause of death in the United States and worldwide. In this paper, we study the bifurcation for a highly nonlinear and highly coupled PDE… read more here.
Keywords: first bifurcation; arterial plaque; free boundary; bifurcation point ... See more keywords
On Trefftz’ integral equation for the Bernoulli free boundary value problem
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DOI: 10.1007/s00211-016-0847-5
Abstract: We propose a new numerical method for the solution of Bernoulli’s free boundary value problem for a harmonic function w in a doubly connected domain D in $$\mathbb {R}^2$$R2 where an unknown free boundary $$\varGamma… read more here.
Keywords: value problem; boundary value; bernoulli free; vargamma ... See more keywords
On the Cheeger problem for rotationally invariant domains
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DOI: 10.1007/s00229-020-01260-9
Abstract: We investigate the properties of the Cheeger sets of rotationally invariant, bounded domains $\Omega \subset \mathbb{R}^n$. For a rotationally invariant Cheeger set $C$, the free boundary $\partial C \cap \Omega$ consists of pieces of Delaunay… read more here.
Keywords: problem rotationally; cheeger problem; invariant domains; rotationally invariant ... See more keywords
On the Banach Manifold of Simple Domains in the Euclidean Space and Applications to Free Boundary Problems
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DOI: 10.1007/s10440-019-00271-3
Abstract: In this paper we study the Banach manifold made up of simple C m + μ $C^{m+\mu }$ -domains in the Euclidean space R n $\mathbb{R}^{n}$ . This manifold is merely a topological or a… read more here.
Keywords: banach manifold; euclidean space; simple domains; free boundary ... See more keywords
Modeling the Relaxation of Oscillations in an Electrolyzer with a Free Boundary
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DOI: 10.1007/s10598-017-9356-3
Abstract: Numerical methods for modeling the behavior of an industrial aluminum electrolyzer are investigated and developed. Solving a prototype problem that brings out the specific features of aluminum electrolysis, we compare two approaches to investigating the… read more here.
Keywords: electrolyzer free; oscillations electrolyzer; relaxation; aluminum electrolysis ... See more keywords
Existence and Uniqueness of an Inverse Memory Kernel for an Integro-Differential Parabolic Equation with Free Boundary
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DOI: 10.1007/s10883-017-9372-9
Abstract: We consider an inverse problem for an integro-differential parabolic equation with free boundary. This inverse problem aims to identify the memory kernel function from a global measurement data. Based on a fixed point argument, we… read more here.
Keywords: parabolic equation; integro differential; differential parabolic; memory kernel ... See more keywords
Domain Walls for the Bénard–Rayleigh Convection Problem with “Rigid–Free” Boundary Conditions
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DOI: 10.1007/s10884-021-09986-0
Abstract: We prove the existence of domain walls for the Benard–Rayleigh convection in the case of “rigid–free” boundary conditions. In the recent work (Haragus and Iooss in Arch Ration Mech Anal 239:733–781, 2021), we studied this… read more here.
Keywords: center manifold; domain walls; rayleigh convection; boundary conditions ... See more keywords
Optimal Control for a Parabolic–Hyperbolic Free Boundary Problem Modeling the Growth of Tumor with Drug Application
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DOI: 10.1007/s10957-016-1037-4
Abstract: In this paper, we study two optimal control problems for a free boundary problem, which models tumor growth with drug application. This free boundary problem is a multicellular tumor spheroid model and includes five time-dependent… read more here.
Keywords: control; drug; boundary problem; optimal control ... See more keywords
Problem with Free Boundary for Systems of Equations of Reaction-Diffusion Type
Sign Up to like & getrecommendations! Published in 2018 at "Ukrainian Mathematical Journal"
DOI: 10.1007/s11253-018-1481-4
Abstract: We consider a problem with free boundary for systems of quasilinear parabolic equations. A part of the boundary conditions is given in the nonlocal form. The a priori estimates of the Hölder norms are established.… read more here.
Keywords: equations reaction; systems equations; problem free; boundary systems ... See more keywords