Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0705.2107

Determination of the body force of a two-dimensional isotropic elastic body

Dang Duc Trong·Alain Pham Ngoc Dinh·Phan Thanh Nam·Truong Trung Tuyen
View original source ↗Read source document ↗Export metadata ↓

Abstract

Let $Ω$ represent a two$-$dimensional isotropic elastic body. We consider the problem of determining the body force $F$ whose form $ϕ(t)(f_1(x),f_2(x))$ with $ϕ$ be given inexactly. The problem is nonlinear and ill-posed. Using the Fourier transform, the methods of Tikhonov's regularization and truncated integration, we construct a regularized solution from the data given inexactly and derive the explicitly error estimate. Numerical part is given

Explore related subjects

math.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Dang Duc Trong, Alain Pham Ngoc Dinh, Phan Thanh Nam, Truong Trung Tuyen. 2008-07-15. Determination of the body force of a two-dimensional isotropic elastic body. https://arxiv.org/abs/0705.2107

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

When Self-Generated Gradients meet Cell Division: Waves and Speed Selection in a Minimal Model

We study a minimal Go-or-Grow model for cell propagation driven by self-generated nutrient gradients, coupling diffusion, division, and directed migration through a discontinuous switching mechanism. We establish local well-posedness, characterize all positive bounded traveling waves, and derive an explicit minimal wave speed. Using neutral fractions, we show that minimal waves undergo a pulled-to-pushed transition as the migratory bias increases, while nonminimal waves remain pulled. Finally, we obtain a weak speed-selection result that singles out the minimal wave speed as the only possible limiting propagation speed.

math.AP↗
arXiv2026

Entropic Chaos of Mixed Mean-Field Jump Processes

This paper studies a class of mixed mean-field jump processes on an abstract state space $Π$, together with their associated $N$-particle systems. The dynamics consist of the superposition of an independent Markovian component and a bounded mean-field jump interaction; in particular, piecewise deterministic Markov processes (PDMPs) with mean-field interactions are covered by this framework. A key feature of our setting is that the jump kernel may depend nonlinearly on the mean-field law, and correspondingly on the empirical measure at the particle level. Under a second-order bounded difference condition on the mean-field jump kernel, we establish entropic propagation of chaos as $N \to \infty$. In particular, we obtain an explicit qualitative bound on the relative entropy between the law of the $N$-particle system and the product measure induced by the mean-field limit. The proof relies on the second-order concentration inequality introduced in Götze and Sambale, 2020.

math.AP↗
arXiv2026

Local profiles of self-similar solutions of the planar stationary Navier--Stokes equations

In this paper, we revisit self-similar solutions of the two-dimensional stationary incompressible Navier-Stokes equations under scaling symmetries, also known as Jeffery-Hamel solutions. We investigate the local patterns of smooth Jeffery-Hamel solutions in a conical subdomain $Ω$ with vertex at the origin, without imposing any boundary conditions on $Ω$. For radial Jeffery-Hamel solutions, we obtain all the explicit local profiles in $Ω$ with arbitrary opening angles. In the non-radial case, we show that some Jeffery-Hamel solutions can be obtained via solving a Liénard equation, and we derive new explicit local profiles expressible in terms of Weierstrass elliptic functions.

math.AP↗