Results 11 to 20 of about 89,092 (266)
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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Analysis of a multiphase free boundary problem [PDF]
Opuscula MathematicaIn this paper, we investigate a free boundary problem relevant in several applications, such as tumor growth models. Our problem is expressed as an elliptic equation involving discontinuous nonlinearities in a specified domain with a moving boundary.
Ahlem Abdelouahab, Sabri Bensid
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Boundary-value problem with free boundary: zirconium alloy hydrogenation
Transactions of the Karelian Research Centre of the Russian Academy of Sciences, 2016 One of the most important requirements for the reactor’s active zone materials (made of zirconium alloys) is low hydrogen absorptivity since hydrogen embrittlement may cause zirconium cladding damage.
Yury Zaika, Natalia Rodchenkova
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Existence of solution of a free boundary problem for reaction-diffusion systems
Современная математика: Фундаментальные направления, 2022 In this paper, we prove the existence of solution of a novel free boundary problem for reaction-diffusion systems describing growth of biological tissues due to cell influx and proliferation.
G. A. Younes +2 more
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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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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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A free boundary problem with nonlinear jump and kinetics on the free boundaries [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 1999 A free boundary problem with nonlinear jump and kinetics on the free boundaries \[ \begin{cases} \Delta u=0\quad & \text{in }\Omega_1(t)=\{(x,y)\in\mathbb{R}^2: g_2(x,t)
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Regularity of the free boundary in the one-phase Stefan problem: a recent approach
Bruno Pini Mathematical Analysis Seminar, 2022 In this note, we discuss about the regularity of the free boundary for the solutions of the one-phase Stefan problem. We start by recalling the classical results achieved by I. Athanasopoulos, L. Caffarelli, and S.
Nicolò Forcillo
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A free boundary problem for an attraction–repulsion chemotaxis system
Boundary Value Problems, 2018 In this paper we study an attraction–repulsion chemotaxis system with a free boundary in one space dimension. First, under some conditions, we investigate existence, uniqueness and uniform estimates of the global solution.
Weiyi Zhang, Zuhan Liu, Ling Zhou
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