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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Boundary conditions for free surface inlet and outlet\ud problems [PDF]
, 2012 We investigate and compare the boundary conditions that are to be applied to free surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes.
Breward, C. J. W. +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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On the Optimal Control of the Free Boundary Problems for the Second Order Parabolic Equations. I.Well-posedness and Convergence of the Method of Lines [PDF]
, 2012 We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary.
Mezzan, Youness, Tber, Moulay Hicham
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Free boundary problems for the diffusive competition system in higher dimension with sign-changing coefficients [PDF]
, 2015 In this article we investigate two free boundary problems for a Lotka-Volterra competition system in a higher space dimension with sign-changing coefficients.
Yonggang Zhao, Mingxin Wang
semanticscholar +1 more source
A new glance to the Alt-Caffarelli-Friedman monotonicity formula
Mathematics in Engineering, 2020 In this paper we revisit the proof of the Alt-Caffarelli-Friedman monotonicity formula. Then, in the framework of the Heisenberg group, we discuss the existence of an analogous monotonicity formula introducing a necessary condition for its existence ...
Fausto Ferrari, Nicolò Forcillo
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Nonlinear Two-Phase Stefan Problem [PDF]
Journal of Sciences, Islamic Republic of Iran, 2007 In this paper we consider a nonlinear two-phase Stefan problem in one-dimensional space. The problem is mapped into a nonlinear Volterra integral equation for the free boundary.
K. Ivaz
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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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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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(Non)local and (non)linear free boundary problems [PDF]
, 2017 We discuss some recent developments in the theory of free boundary problems, as obtained in a series of papers in collaboration with L. Caffarelli, A. Karakhanyan and O. Savin.
Dipierro, Serena, Valdinoci, Enrico
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