Results 21 to 30 of about 96 (92)

Well‐Posedness, Long‐Time Behavior, and Discretization of Some Models of Nonlinear Acoustics in Velocity–Enthalpy Formulation

Mathematical Methods in the Applied Sciences, Volume 48, Issue 8, Page 8793-8805, 30 May 2025.
ABSTRACT We study a class of models for nonlinear acoustics, including the well‐known Westervelt and Kuznetsov equations, as well as a model of Rasmussen that can be seen as a thermodynamically consistent modification of the latter. Using linearization, energy estimates, and fixed‐point arguments, we establish the existence and uniqueness of solutions ...
Herbert Egger, Marvin Fritz
wiley   +1 more source

A Robust Exponentially Fitted Scheme for Singularly Perturbed Fractional‐Order Delay Parabolic Equation

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
This study introduces a fitted numerical approach for solving singularly perturbed time‐fractional parabolic differential equations incorporating a delay term. The stability of the method is rigorously examined using the comparison principle and solution bounds, while its convergence is analyzed through the barrier function approach and the Peano ...
Nuru Ahmed Endrie, Gemechis File Duressa, Mohammad Mirzazadeh   +2 more
wiley   +1 more source

Flow Matching with Semidiscrete Couplings

CoRR
Flow models parameterized as time-dependent velocity fields can generate data from noise by integrating an ODE. These models are often trained using flow matching, i.e. by sampling random pairs of noise and target points $(\mathbf{x}_0,\mathbf{x}_1)$ and ensuring that the velocity field is aligned, on average, with $\mathbf{x}_1-\mathbf{x}_0$ when ...
Alireza Mousavi Hosseini, Stephen Y. Zhang, Michal Klein, Marco Cuturi   +3 more
openaire   +2 more sources

Fitted Operator Method for Singularly Perturbed Delay Parabolic Problems With Boundary Turning Points

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
In this paper, a numerical scheme for time‐delay singularly perturbed parabolic convection‐diffusion problems with boundary turning points is presented. The solution of the problem shows a steep gradient or rapid variation at the left region of the spatial domain as the perturbation parameter approaches zero.
Yimesgen Mehari Kebede, Awoke Andargie Tiruneh, Endalew Getnet Tsega, Nian-Sheng Tang   +3 more
wiley   +1 more source

Finite and Infinitesimal Flexibility of Semidiscrete Surfaces [PDF]

Arnold Mathematical Journal, 2015
In this paper we study infinitesimal and finite flexibility for generic semidiscrete surfaces. We prove that generic 2-ribbon semidiscrete surfaces have one degree of infinitesimal and finite flexibility. In particular we write down a system of differential equations describing isometric deformations in the case of existence.
openaire   +3 more sources

Hybrid Fitted Mesh Strategy for Singularly Perturbed Time‐Dependent Convection‐Diffusion Problems Featuring Boundary Turning Points

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
This work investigates the solution of convection‐diffusion parabolic partial‐differential problems with boundary turning points that are singularly perturbed. These types of problems are stiff for the following reason: the small parameter multiplying coefficient of the diffusion term and the presence of boundary turning points.
Yimesgen Mehari Kebede, Awoke Andargie Tiruneh, Endalew Getnet Tsega, Mohamed A. Eltaher   +3 more
wiley   +1 more source

A Uniformly Convergent Scheme for Singularly Perturbed Unsteady Reaction–Diffusion Problems

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
In the present work, a class of singularly perturbed unsteady reaction–diffusion problem is considered. With the existence of a small parameter ε, (0 < ε ≪ 1) as a coefficient of the diffusion term in the proposed model problem, there exist twin boundary layer regions near the left end point x = 0 and right end point x = 1 of the spatial domain.
Amare Worku Demsie, Awoke Andargie Tiruneh, Endalew Getnet Tsega, Tudor Barbu   +3 more
wiley   +1 more source

An Exponentially Fitted Upwind Scheme for Singularly Perturbed Differential Equations With Mixed Shift Parameters

Journal of Mathematics, Volume 2025, Issue 1, 2025.
This paper provides numerical solutions to a class of singularly perturbed differential–difference equations characterized by mixed shift parameters. The solutions of such problems exhibit sharp boundary layers near the endpoints of the spatial domain due to the presence of a small perturbation parameter ε(0 < ε ≪ 1).
Amare Worku Demsie, Awoke Andargie Tiruneh, Endalew Getnet Tsega, Luigi Rarità   +3 more
wiley   +1 more source

Regularizations of forward‐backward parabolic PDEs

GAMM-Mitteilungen, Volume 47, Issue 4, November 2024.
Abstract Forward‐backward parabolic equations have been studied since the 1980s, but a mathematically rigorous picture is still far from being established. As quite a number of new papers have appeared recently, we review in this work the current state of the art.
Carina Geldhauser
wiley   +1 more source

Space–time finite element method with domain reduction techniques for dynamic soil–structure interaction problems

International Journal of Mechanical System Dynamics, Volume 4, Issue 2, Page 117-130, June 2024.
Abstract Design of earth structures, such as dams, tunnels, and embankments, against the vibrational loading caused by high‐speed trains, road traffic, underground explosions, and, more importantly, earthquake motion, demands solutions of the dynamic soil–structure Interaction (SSI) problem.
Vikas Sharma, Shion Shimizu, Kazunori Fujisawa   +2 more
wiley   +1 more source