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Free boundary problem for predator-prey model [PDF]
E3S Web of Conferences, 2023 In this article, we study the behavior of two species evolving in a domain with a free boundary. This system mimics the spread of invasive or new predator species, in which free boundaries represent the expanding fronts of predator species and are ...
Elmurodov Alimardon +4 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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Properties of the free boundary near the fixed boundary of the double obstacle problems
Bulletin of Mathematical Sciences, 2022 In this paper, we study the tangential touch and [Formula: see text] regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator.
Jinwan Park
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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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Asymptotic Behavior of Solutions to Free Boundary Problem with Tresca Boundary Conditions
Journal of Function Spaces, 2021 In this paper, we study the asymptotic behavior of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions. We study the limit when the ε tends to zero, we prove the convergence of the unknowns which are the velocity and
Abdelkader Saadallah +5 more
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Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics
Mathematics, 2021 In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. An electromagnetic field generated by some currents in an external domain keeps an MHD flow in a bounded domain. On
Kenta Oishi, Yoshihiro Shibata
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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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Regularity results for a quasilinear free boundary problem
Mathematical Modelling and Analysis, 2020 In this paper we prove local interior and boundary Lipschitz continuity of the solutions of a quasilinear free boundary problem. We also show that the free boundary is the union of graphs of lower semi-continuous functions.
Samia Challal, Abdeslem Lyaghfouri
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On a Multistable Type of Free Boundary Problem with a Flux at the Boundary
Advances in Mathematical Physics, 2023 This paper studies the free boundary problem of a multistable equation with a Robin boundary condition, which may be used to describe the spreading of the invasive species with the solution representing the density of species and the free boundary ...
Haitao Ren, Jingjing Cai, Li Xu
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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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