Results 41 to 50 of about 120,918 (284)

Numerical Reconstruction of the Source in Dynamical Boundary Condition of Laplace’s Equation

Axioms
In this work, we consider Cauchy-type problems for Laplace’s equation with a dynamical boundary condition on a part of the domain boundary. We construct a discrete-in-time, meshless method for solving two inverse problems for recovering the space–time ...
Miglena N. Koleva, Lubin G. Vulkov
doaj   +1 more source

The existence of positive solutions for an elliptic boundary value problem

International Journal of Mathematics and Mathematical Sciences, 2005
By using the mountain pass lemma, we study the existence of positive solutions for the equation −Δu(x)=λ(u|u|+u)(x) for x∈Ω together with Dirichlet boundary conditions and show that for every ...
G. A. Afrouzi
doaj   +1 more source

An Asymptotic Formalism for Reconstructing Small Perturbations of Scatterers from Electric or Acoustic Far-Field Measurements [PDF]

, 2007
We consider the problem of determining the boundary perturbations of an object from far-field electric or acoustic measurements. Assuming that the unknown object boundary is a small perturbation of a circle, we develop a linearized relation between the ...
Abrohmwitz, Ammari, Coifman, Colton, Kaup, Milder, Nicholls, Tolmasky   +7 more
core   +3 more sources

CFD modeling and sensitivity‐guided design of silicon filament CVD reactors

AIChE Journal, EarlyView.
Abstract Filament‐based chemical vapor deposition (CVD) for silicon (Si) coatings is often treated as an adaptation of planar deposition. But this overlooks fundamental shifts in transport phenomena and reaction kinetics. In filament CVD, the filament acts as a substrate, heat source, and flow disruptor simultaneously. In this work, we ask: What really
G. P. Gakis, G. Loachamín‐Suntaxi, I. G. Aviziotis, E. D. Koronaki, P. P. Filippatos, G. Chatzigiannakis, S. P. A. Bordas, D. Davazoglou, A. G. Boudouvis   +8 more
wiley   +1 more source

Large time behavior of solutions of viscous Hamilton-Jacobi Equations with superquadratic Hamiltonian [PDF]

, 2009
We study the long-time behavior of the unique viscosity solution $u$ of the viscous Hamilton-Jacobi Equation $u_t-\Delta u + |Du|^m = f\hbox{in }\Omega\times (0,+\infty)$ with inhomogeneous Dirichlet boundary conditions, where $\Omega$ is a bounded ...
Tchamba, Thierry Wilfried Tabet
core   +3 more sources

Homogenization of the planar waveguide with frequently alternating boundary conditions

, 2009
We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary.
Borisov D, Borisov D, Borisov D, Borisov D I, Brillard A, Chechkin G A, D Borisov, Damlamian A, Davies E B, Exner P, G Cardone, Gadyl'shin R R, Kuchment P, Ladyzhenskaya O A, Ladyzhenskaya O A, Olejnik O A, Reed M, Reed M, Zhikov V V   +18 more
core   +1 more source

RAMS: Residual‐Based Adversarial‐Gradient Moving Sample Method for Scientific Machine Learning in Solving Partial Differential Equations

Advanced Intelligent Discovery, EarlyView.
We propose a residual‐based adversarial‐gradient moving sample (RAMS) method for scientific machine learning that treats samples as trainable variables and updates them to maximize the physics residual, thereby effectively concentrating samples in inadequately learned regions.
Weihang Ouyang, Min Zhu, Wei Xiong, Si‐Wei Liu, Lu Lu   +4 more
wiley   +1 more source

The Approximate Solution of 2D Dirichlet Problem in Doubly Connected Domains

Advances in Mathematical Physics, 2018
We propose a new method for constructing an approximate solution of the two-dimensional Laplace equation in an arbitrary doubly connected domain with smooth boundaries for Dirichlet boundary conditions.
Atallah El-shenawy, Elena A. Shirokova
doaj   +1 more source

Casimir pistons with hybrid boundary conditions

, 2007
The Casimir effect giving rise to an attractive or repulsive force between the configuration boundaries that confine the massless scalar field is reexamined for one to three-dimensional pistons in this paper.
H. B. G. Casimir, Xiang-hua Zhai, Xin-zhou Li   +2 more
core   +1 more source

A Stochastic Conservation Law with Nonhomogeneous Dirichlet Boundary Conditions [PDF]

Acta Mathematica Vietnamica, 2015
This paper discusses the initial-boundary value problem (with a nonhomogeneous boundary condition) for a multi-dimensional scalar first-order conservation law with a multiplicative noise. One introduces a notion of kinetic formulations in which the kinetic defect measures on the boundary of a domain are truncated.
Kobayasi, Kazuo, Noboriguchi, Dai
openaire   +3 more sources