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Optimal approximations for the free boundary problems of the space-time fractional Black-Scholes equations using a combined physics-informed neural network [PDF]
Scientific ReportsThe combined physics-informed neural network is employed to deal with the free boundary problems of fractional Black-Scholes equations. The solution assumption and the loss function are determined, the transfer learning is borrowed, the combined neural ...
Lina Song +4 more
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Multidimensional transonic shock waves and free boundary problems
Bulletin of Mathematical Sciences, 2022 We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for the Euler equations in compressible fluid dynamics.
Gui-Qiang G. Chen, Mikhail Feldman
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Free boundary problems in the spirit of Sakai’s theorem
Comptes Rendus. Mathématique, 2022 A Schwarz function on an open domain $\Omega $ is a holomorphic function satisfying $S(\zeta )=\bar{\zeta }$ on $\Gamma $, which is part of the boundary of $\Omega $.
Vardakis, Dimitris, Volberg, Alexander
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Branch points for (almost-)minimizers of two-phase free boundary problems
Forum of Mathematics, Sigma, 2023 We study the existence and structure of branch points in two-phase free boundary problems. More precisely, we construct a family of minimizers to an Alt–Caffarelli–Friedman-type functional whose free boundaries contain branch points in the strict ...
Guy David +3 more
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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 a Casson Fluid Motion: Nonuniform Width Symmetric Channel and Peristaltic Flows
Fluids, 2021 Widely used for modeling biological fluids flows—in particular, blood vessel flows—a Casson flow is studied in a symmetric channel for which the aspect ratio enables one to use the lubrication approximation.
Simone Guadagni +3 more
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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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Mathematics, 2023 The research on free surface flow is of great interest in fluid mechanics, with the primary task being the tracking and description of the motion of free surfaces.
Kaixuan Shao, Yinghan Wu, Suizi Jia
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Schrödinger-type identity for Schrödinger free boundary problems
Boundary Value Problems, 2018 Our aim in this paper is to develop a Schrödinger-type identity for a Schrödinger free boundary problem in Rn $\mathbb{R}^{n}$. As an application, we establish necessary and sufficient conditions for the product of some distributional functions to ...
Xingjian Zhang +4 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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