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Multiple solutions are common in various non-convex problems arising from industrial and scientific computing. Nonetheless, understanding the nontrivial solutions' qualitative properties seems limited, partially due to the lack of efficient…

Numerical Analysis · Mathematics 2025-04-17 Yangyi Ye , Lin Li , Pengcheng Xie , Haijun Yu

We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…

Numerical Analysis · Mathematics 2021-08-09 Andrea Bonito , Vivette Girault , Diane Guignard , Kumbakonam R. Rajagopal , Endre Süli

In the framework of non-riemannian geometry, we derive exact static vacuum solutions of the field equations obtained from the full equivalent version of the Einstein-Hilbert action when torsion degrees of freedom are taken into account. By…

General Relativity and Quantum Cosmology · Physics 2014-12-16 Rodrigo Maier

This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first…

Quantum Physics · Physics 2020-01-22 Andre G. Campos , Renan Cabrera

A (linear) nonsingular solution for the edge dislocation in the translational gauge theory of defects is presented. The stress function method is used and a modified stress function is obtained. All field quantities are globally defined and…

Materials Science · Physics 2008-11-26 Markus Lazar

The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions…

Analysis of PDEs · Mathematics 2017-10-30 Simone Calogero , Stephen Pankavich

We consider the Cauchy problem for 2-D incompressible isotropic elastodynamics. Standard energy methods yield local solutions on a time interval $[0,{T}/{\epsilon}]$, for initial data of the form $\epsilon U_0$, where $T$ depends only on…

Analysis of PDEs · Mathematics 2013-01-01 Zhen Lei , Thomas C. Sideris , Yi Zhou

The inverse problem of plane elasticity on $n$ equal-strength cavities in a plane subjected to constant loading at infinity and in the cavities boundary is analyzed. By reducing the governing boundary value problem to the Riemann-Hilbert…

Complex Variables · Mathematics 2017-12-20 Yuri A. Antipov

We consider planar liquid crystal elastomers: two dimensional objects made of anisotropic responsive materials, that upon activation remain flat however change their planar shape. We derive a closed form, analytical solution based on the…

Soft Condensed Matter · Physics 2023-05-02 Daniel Castro , Hillel Aharoni

We introduce and study a new inverse problem for antiplane shear in elastic bodies with strain-gradient interfaces. The setting is a homogeneous isotropic elastic body containing an inclusion separated by a thin interface endowed with…

Analysis of PDEs · Mathematics 2025-09-19 Govanni Granados , Jeremy L. Marzuola , Casey Rodriguez

We establish a rigidity theorem for annular sector-like domains in the setting of overdetermined elliptic problems on model Riemannian manifolds. Specifically, if such a domain admits a solution to the inhomogeneous Helmholtz equation…

Analysis of PDEs · Mathematics 2025-06-03 João Marcos do Ó , Jaqueline de Lima , Márcio Santos

The stress fields of dislocations predicted by classical elasticity are known to be unrealistically large approaching the dislocation core, due to the singular nature of the theory. While in many cases this is remedied with the…

Materials Science · Physics 2015-05-22 Dariush Seif , Giacomo Po , Matous Mrovec , Markus Lazar , Christian Elsaesser , Peter Gumbsch

Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…

Numerical Analysis · Mathematics 2018-05-01 Yue Mei , Daniel E. Hurtado , Sanjay Pant , Ankush Aggarwal

We derive the rate-form spatial equilibrium system for a nonlinear Cauchy elastic formulation in isotropic finite-strain elasticity. For a given explicit Cauchy stress-strain constitutive equation, we determine those properties that pertain…

Analysis of PDEs · Mathematics 2025-09-16 Patrizio Neff , Nina J. Husemann , Sebastian Holthausen , Franz Gmeineder , Thomas Blesgen

This paper presents an extension of the unfolding operator technique, initially applied to two-dimensional domains, to the realm of three-dimensional thin domains. The advancement of this methodology is pivotal, as it enhances our…

Analysis of PDEs · Mathematics 2024-05-10 José M. Arrieta , Jean Carlos Nakasato , Manuel Villanueva-Pesqueira

In this work a novel approach is presented for the isogeometric Boundary Element analysis of domains that contain inclusions with different elastic properties than the ones used for computing the fundamental solutions. In addition the…

Numerical Analysis · Computer Science 2016-08-24 Gernot Beer , Benjamin Marussig , Jürgen Zechner , Christian Dünser , Thomas-Peter Fries

We propose a novel efficient algorithm to solve Poisson equation in irregular two dimensional domains for electrostatics. It can handle Dirichlet, Neumann or mixed boundary problems in which the filling media can be homogeneous or…

Mathematical Physics · Physics 2013-06-17 Zu-Hui Ma , Weng Cho Chew , Li Jun Jiang

Near the singularity, gravity should be modified to an effective theory, in the same sense as with the Euler-Heisenberg electrodynamics. This effective gravity surmounts to higher derivative theory, and as is well known, a much more reacher…

General Relativity and Quantum Cosmology · Physics 2013-08-02 Daniel Müller

Motivated by the existing complications of finding solutions of Eringen nonlocal model, an alternative model is developed here. The new formulation of the nonlocal elasticity is centered upon expressing the dynamic equilibrium requirements…

Applied Physics · Physics 2018-10-11 Mohamed Shaat

We study the behaviour of solutions of linear non-autonomous parabolic equations subject to Dirichlet or Neumann boundary conditions under perturbation of the domain. We prove that Mosco convergence of function spaces for non-autonomous…

Analysis of PDEs · Mathematics 2011-09-16 Parinya Sa Ngiamsunthorn