Results 21 to 30 of about 9,189,330 (242)
Some Free Boundary Problems Arising in Rock Mechanics
Современная математика: Фундаментальные направления, 2018 В этой статье мы рассматриваем несколько физических процессов в механике горных пород, которые описываются задачами со свободной границей. Некоторые из них известны (задачи Муската), другие совершенно новые (подземное выщелачивание и динамика трещин в ...
A M Meirmanov, O V Galtsev, O A Galtseva
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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 second order convergent trial method for a free boundary problem in three dimensions [PDF]
, 2015 The present article is concerned with the solution of a generalized Bernoulli free boundary problem in three spatial dimensions. We parametrize the free boundary under consideration over the sphere and apply a trial method which updates the free boundary
Harbrecht, Helmut, Bugeanu, Monica
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Two-Phase Free Boundary Problems: From Existence to Smoothness
Advanced Nonlinear Studies, 2017 We describe the theory we developed in recent times concerning two-phasefree boundary problems governed by elliptic operators with forcing terms.Our results range from existence of viscosity solutions to smoothness ofboth solutions and free boundaries ...
De Silva Daniela +2 more
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An elliptic problem of the Prandtl–Batchelor type with a singularity
Boundary Value Problems, 2023 We establish the existence of at least two solutions of the Prandtl–Batchelor like elliptic problem driven by a power nonlinearity and a singular term. The associated energy functional is nondifferentiable, and hence the usual variational techniques do ...
Debajyoti Choudhuri, Dušan D. Repovš
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Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth [PDF]
, 2008 We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth.
Varvaruca, Eugen
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Compactness estimates for minimizers of the Alt-Phillips functional of negative exponents
Advanced Nonlinear Studies, 2023 We investigate the rigidity of global minimizers u≥0u\ge 0 of the Alt-Phillips functional involving negative power potentials ∫Ω(∣∇u∣2+u−γχ{u>0})dx,γ∈(0,2),\mathop{\int }\limits_{\Omega }(| \nabla u{| }^{2}+{u}^{-\gamma }{\chi }_{\left\{u\gt 0\right\}}){\
De Silva Daniela, Savin Ovidiu
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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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Improved trial methods for a class of generalized Bernoulli problems [PDF]
, 2013 The aim of this article is to develop improved trial methods for the solution of a generalized exterior Bernoulli free boundary problem. At the free boundary, we prescribe the Neumann boundary condition and update the free boundary with the help of the ...
Mitrou, Giannoula, Harbrecht, Helmut
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