Multidimensional transonic shock waves and free boundary problems [PDF]
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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PDE methods for free boundary problems in financial mathematics
, 2008 We consider different aspects of free boundary problems that have financial applications. Papers I–III deal with American option pricing, in which case the boundary is called the early exercise boundary and separates the region where to hold the option from the region where to exercise it.
Teitur Arnarson
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Energy Methods for Free Boundary Problems: Applications to Nonlinear PDEs and Fluid Mechanics. Progress in Nonlinear Differential Equations and Their Applications, Vol 48 [PDF]
Applied Mechanics Reviews, 2002 SN Antontsev, +3 more
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Finite line method for solving high-order partial differential equations in science and engineering
Partial Differential Equations in Applied Mathematics, 2023 In this paper, a completely new numerical method, named Finite Line Method (FLM), is proposed for solving general linear and non-linear high-order partial differential equations (PDEs) in science as well as engineering problems in heat conduction and ...
Xiao-Wei Gao, Yu-Mo Zhu, Tao Pan
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Nonlinear Pantograph-Type Diffusion PDEs: Exact Solutions and the Principle of Analogy
Mathematics, 2021 We study nonlinear pantograph-type reaction–diffusion PDEs, which, in addition to the unknown u=u(x,t), also contain the same functions with dilated or contracted arguments of the form w=u(px,t), w=u(x,qt), and w=u(px,qt), where p and q are the free ...
Andrei D. Polyanin, Vsevolod G. Sorokin
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Extending Density Phase-Field Simulations to Dynamic Regimes
Metals, 2023 Density-based phase-field (DPF) methods have emerged as a technique for simulating grain boundary thermodynamics and kinetics. Compared to the classical phase-field, DPF gives a more physical description of the grain boundary structure and chemistry ...
David Jacobson +2 more
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MethodsX, 2022 This article presents a new approximation of order four in exponential form for two-dimensional (2D) quasilinear partial differential equation (PDE) of elliptic form with solution domain being irrational.
R.K. Mohanty +3 more
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Geometry aware physics informed neural network surrogate for solving Navier–Stokes equation (GAPINN)
Advanced Modeling and Simulation in Engineering Sciences, 2022 Many real world problems involve fluid flow phenomena, typically be described by the Navier–Stokes equations. The Navier–Stokes equations are partial differential equations (PDEs) with highly nonlinear properties. Currently mostly used methods solve this
Jan Oldenburg +4 more
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PDE problems arising in mathematical biology
Networks and Heterogeneous Media, 2012 This article reviews biological processes that can be modeled by PDEs, it describes mathematical results, and suggests open problems. The first topic deals with tumor growth.
Avner Friedman
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MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework [PDF]
, 2020 We propose MeshfreeFlowNet, a novel deep learning-based super-resolution framework to generate continuous (grid-free) spatio-temporal solutions from the low-resolution inputs. While being computationally efficient, MeshfreeFlowNet accurately recovers the
Anandkumar, Anima +8 more
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