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The two-dimensional nonlinear problem of steady flow past a body submerged beneath an elastic sheet is considered. The mathematical model is based on the velocity potential theory with fully nonlinear boundary conditions on the fluid…

Fluid Dynamics · Physics 2021-06-16 Y. A. Semenov

We consider the problem of 2D supersonic flow onto a solid wedge, or equivalently in a concave corner formed by two solid walls. For mild corners, there are two possible steady state solutions, one with a strong and one with a weak shock…

Mathematical Physics · Physics 2009-09-29 Volker Elling , Tai-Ping Liu

In this paper, we study the problem of shock reflection by a wedge, with the potential flow equation, which is a simplification of the Euler System. In the work of M. Feldman and G. Chen, the existence theory of shock reflection problems…

Analysis of PDEs · Mathematics 2021-03-31 Jingchen Hu

The problem of a cold gas flowing past a stationary object is considered. It is shown that at large distances from the obstacle the shock front forms a parabolic solid of revolution. The interior of the shock front is obtained by solution…

High Energy Astrophysical Phenomena · Physics 2016-08-17 Almog Yalinewich , Re'em Sari

In this paper, we prove the existence of two-dimensional solutions to the steady Euler-Poisson system with continuous transonic transitions across sonic interfaces of codimension 1. First, we establish the well-posedness of a boundary value…

Analysis of PDEs · Mathematics 2023-08-10 Myoungjean Bae , Ben Duan , Chunjing Xie

This brief note addresses the free boundary problem arising from the steady two-dimensional seepage flow through a rectangular dam. The flow problem consists in finding the free boundary location, and the velocity and pressure fields. The…

Fluid Dynamics · Physics 2015-07-21 Carmine Di Nucci

This paper concerns with the existence of transonic shocks for steady Euler flows in a 3-D axisymmetric cylindrical nozzle, which are governed by the Euler equations with the slip boundary condition on the wall of the nozzle and a receiver…

Analysis of PDEs · Mathematics 2020-09-30 Beixiang Fang , Xin Gao

An asymptotic analysis of the Gunn effect in two-dimensional samples of bulk n-GaAs with circular contacts is presented. A moving pulse far from contacts is approximated by a moving free boundary separating regions where the electric…

Materials Science · Physics 2009-11-10 L. L. Bonilla , R. Escobedo , F. J. Higuera

We are concerned with a two-dimensional ($2$-D) Riemann problem for compressible flows modeled by the pressure gradient system that is a $2$-D hyperbolic system of conservation laws. The Riemann initial data consist of four constant states…

Analysis of PDEs · Mathematics 2020-08-26 Gui-Qiang G. Chen , Qin Wang , Shengguo Zhu

We consider the boundary rigidity problem for asymptotically hyperbolic manifolds. We show injectivity of the X-ray transform in several cases and consider the non-linear inverse problem which consists of recovering a metric from boundary…

Differential Geometry · Mathematics 2017-09-18 C. Robin Graham , Colin Guillarmou , Plamen Stefanov , Gunther Uhlmann

In this paper, we are concerned with the existence of transonic shock solutions for two-dimensional (2-d) steady Euler flows of polytropic gases with the vertical gravity in a horizontal nozzle under a pressure condition imposed at the exit…

Analysis of PDEs · Mathematics 2025-04-08 Beixiang Fang , Xin Gao , Wei Xiang , Qin Zhao

Although local existence of multidimensional shock waves has been established in some fundamental references, there are few results on the global existence of those waves except the ones for the unsteady potential flow equations in…

Analysis of PDEs · Mathematics 2013-10-15 Jun Li , Ingo Witt , Huicheng Yin

This study aims to shed light on hypersonic attachment-line instabilities with large sweep Mach numbers. Highly swept flows over a cold cylinder that give rise to large sweep Mach numbers are studied. High fidelity base flows are obtained…

Fluid Dynamics · Physics 2021-07-01 Youcheng Xi , Jie Ren , Song Fu

In this work, we study the eigenvalue problem associated with the bidomain operator in an anisotropic heterogeneous domain composed of three subregions representing the left ventricle, the septum, and the right ventricle. The anisotropic…

Analysis of PDEs · Mathematics 2026-04-07 Raul Felipe-Sosa , Yofre H. García-Gómez

We investigate the hypersonic limit for steady, uniform, and compressible polytropic gas passing a symmetric straight cone. By considering Radon measure solutions, we show that as the Mach number of the upstream flow tends to infinity, the…

Analysis of PDEs · Mathematics 2024-04-17 Qianfeng Li , Aifang Qu , Xueying Su , Hairong Yuan

We propose a method of construction of exact solutions of free boundary problems corresponding to Hele-Shaw flows in presence of an external field. Such a field may arise, in particular, due to electrokinetic phenomena. Both a general…

Mathematical Physics · Physics 2007-05-23 Vladimir Entov , Pavel Etingof

An initial boundary value problem for one-dimensional hyperbolic compressible Navier-Stokes equations is investigated. After transforming the system into Lagrangian coordinate, the resulting system possesses a structure with uniform…

Analysis of PDEs · Mathematics 2025-08-05 Yuxi Hu , Yachun Li

We construct a supersonic-sonic smooth patch solution for the two dimensional steady Euler equations in gas dynamics. This patch is extracted from the Frankl problem in the study of transonic flow with local supersonic bubble over an…

Analysis of PDEs · Mathematics 2021-01-05 Yanbo Hu , Jiequan Li

We proposed rigorous definitions of Radon measure solutions for boundary value problems of steady compressible Euler equations which modeling hypersonic-limit inviscid flows passing two-dimensional ramps, and their interactions with still…

Analysis of PDEs · Mathematics 2019-09-10 Yunjuan Jin , Aifang Qu , Hairong Yuan

This paper concerns compressible subsonic jet flows for a given surrounding pressure from a two-dimensional finitely long convergent nozzle with straight solid wall, which are governed by a free boundary problem for a quasilinear elliptic…

Analysis of PDEs · Mathematics 2019-02-08 Chunpeng Wang , Zhouping Xin