Results 11 to 20 of about 64,585 (264)
New Trends in Free Boundary Problems [PDF]
Advanced Nonlinear Studies, 2017 We present a series of recent results on some new classes of free boundary problems.Differently from the classical literature, the problems considered have either a “nonlocal” feature (e.g., the interaction or/and the interfacial energy may depend on ...
Dipierro Serena +2 more
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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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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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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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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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A remark on memory effects in constrained fluid systems [PDF]
ESAIM: Proceedings and Surveys, 2020 The goal of this note is to put into perspective the recent results obtained on memory effects in partially congested fluid systems of Euler or Navier-Stokes type with former studies on free boundary obstacle problems and Hele-Shaw equations.
Perrin Charlotte
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Free boundary problems in biology [PDF]
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015 In this paper, I review several free boundary problems that arise in the mathematical modelling of biological processes. The biological topics are quite diverse: cancer, wound healing, biofilms, granulomas and atherosclerosis. For each of these topics, I describe the biological background and the mathematical model, and then proceed to state ...
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Perturbation in a Free Boundary Problem
Journal of Mathematical Analysis and Applications, 1994 This paper is concerned with the Dirichlet boundary value problem for a semilinear elliptic partial differential equation with a discontinuous nonlinearity on the unit ball \(B\) in \(\mathbb{R}^2\). Precisely, the authors consider the problem for \(u\) with two positive parameters \(\lambda\) and \(\varepsilon\): \[ - \Delta u= (\lambda+ \varepsilon g(
Boucherif, Abdelkader, Bouguima, Mohamed
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On Plateau's Problem with Free Boundaries [PDF]
Proceedings of the National Academy of Sciences, 1945 Not ...
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