Results 21 to 30 of about 1,011,292 (311)
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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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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Well-posedness of the free boundary problem in compressible elastodynamics [PDF]
, 2017 We study the free boundary problem for the flow of a compressible isentropic inviscid elastic fluid. At the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary and the pressure
Y. Trakhinin
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Regularity of the free boundary for the two-phase Bernoulli problem [PDF]
Inventiones Mathematicae, 2019 We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s.
G. De Philippis +2 more
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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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Well-posedness of the free boundary problem in incompressible elastodynamics
Journal of Differential Equations, 2019 In this paper, we prove the local well-posedness of the free boundary problem in incompressible elastodynamics under a natural stability condition, which ensures that the evolution equation describing the free boundary is strictly hyperbolic.
Hui Li, Wei Wang, Zhifei Zhang
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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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Analysis of a free boundary problem modeling the growth of multicell spheroids with angiogenesis
Journal of Differential Equations, 2018 In this paper we study a free boundary problem modeling the growth of vascularized tumors. The model is a modification to the Byrne–Chaplain tumor model that has been intensively studied during the past two decades.
Yuehong Zhuang, S. Cui
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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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