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Multidimensional transonic shock waves and free boundary problems
Bulletin of Mathematical Sciences, 2022 We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for the Euler equations in compressible fluid dynamics.
Gui-Qiang G. Chen, Mikhail Feldman
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A Nonlocal Free Boundary Problem [PDF]
SIAM Journal on Mathematical Analysis, 2015 Given~$s,σ\in(0,1)$ and a bounded domain~$Ω\subset\R^n$, we consider the following minimization problem of $s$-Dirichlet plus $σ$-perimeter type $$ [u]_{ H^s(\R^{2n}\setminus(Ω^c)^2) } + \Per_σ\left(\{u>0\},Ω\right), $$ where~$[ \cdot]_{H^s}$ is the fractional Gagliardo seminorm and $\Per_σ$ is the fractional perimeter. Among other results, we prove
S. Dipierro, O. Savin, E. Valdinoci
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Free boundary problems in the spirit of Sakai’s theorem
Comptes Rendus. Mathématique, 2022 A Schwarz function on an open domain $\Omega $ is a holomorphic function satisfying $S(\zeta )=\bar{\zeta }$ on $\Gamma $, which is part of the boundary of $\Omega $.
Vardakis, Dimitris, Volberg, Alexander
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Branch points for (almost-)minimizers of two-phase free boundary problems
Forum of Mathematics, Sigma, 2023 We study the existence and structure of branch points in two-phase free boundary problems. More precisely, we construct a family of minimizers to an Alt–Caffarelli–Friedman-type functional whose free boundaries contain branch points in the strict ...
Guy David +3 more
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ON BERNOULLI'S FREE BOUNDARY PROBLEM WITH A RANDOM BOUNDARY [PDF]
International Journal for Uncertainty Quantification, 2017 This article is dedicated to the solution of Bernoulli’s exterior free boundary problem in the situation of a random interior boundary. We provide the theoretical background that ensures the well-posedness of the problem under consideration and describe two different frameworks to define the expectation and the deviation of the resulting annular domain.
Dambrine, Marc +3 more
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Properties of the free boundary near the fixed boundary of the double obstacle problems
Bulletin of Mathematical Sciences, 2022 In this paper, we study the tangential touch and [Formula: see text] regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator.
Jinwan Park
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Free boundaries in problems with hysteresis [PDF]
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015 Here, we present a survey concerning parabolic free boundary problems involving a discontinuous hysteresis operator. Such problems describe biological and chemical processes ‘with memory’ in which various substances interact according to hysteresis law.
D. E. Apushkinskaya, N. N. Uraltseva
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A Free Boundary Problem with Facets [PDF]
Archive for Rational Mechanics and Analysis, 2018 38 pages, 2 ...
William M. Feldman, Charles K. Smart
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On a Casson Fluid Motion: Nonuniform Width Symmetric Channel and Peristaltic Flows
Fluids, 2021 Widely used for modeling biological fluids flows—in particular, blood vessel flows—a Casson flow is studied in a symmetric channel for which the aspect ratio enables one to use the lubrication approximation.
Simone Guadagni +3 more
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Crack Propagation as a Free Boundary Problem [PDF]
Physical Review Letters, 2007 A newly developed sharp interface model describes crack propagation by a phase transition process. We solve this free boundary problem numerically and obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic effects are taken into account.
Müller-Krumbhaar, H. +3 more
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