Results 111 to 120 of about 110,294 (285)

Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case

Electronic Journal of Differential Equations, 2004
We derive a monotonicity formula at boundary points for a class of nonlinear elliptic partial differential equations, including the obstacle problem case, quenching, a free boundary problem with Bernoulli-type free boundary condition as well as the blow ...
Georg S. Weiss
doaj  

Shape Derivatives of the Eigenvalues of the De Rham Complex for Lipschitz Deformations and Variable Coefficients: Part I

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We study eigenvalue problems for the de Rham complex on varying three‐dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed boundary conditions and non‐constant coefficients. We provide Hadamard‐type formulas for the shape derivatives under weak regularity assumptions on the domain and its ...
Pier Domenico Lamberti, Dirk Pauly, Michele Zaccaron   +2 more
wiley   +1 more source

Asymptotics for the Spectrum of the Laplacian in Thin Bars with Varying Cross Sections

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We consider spectral problems for the Laplace operator in 3D rod structures with a small cross section of diameter O(ε)$$ O\left(\varepsilon \right) $$, ε$$ \varepsilon $$ being a positive parameter. The boundary conditions are Dirichlet (Neumann, respectively) on the bases of this structure, and Neumann on the lateral boundary.
Pablo Benavent‐Ocejo, Delfina Gómez, Maria‐Eugenia Pérez‐Martínez   +2 more
wiley   +1 more source

Existence Analysis of a Three‐Species Memristor Drift‐Diffusion System Coupled to Electric Networks

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT The existence of global weak solutions to a partial‐differential‐algebraic system is proved. The system consists of the drift‐diffusion equations for the electron, hole, and oxide vacancy densities in a memristor device, the Poisson equation for the electric potential, and the differential‐algebraic equations for an electric network.
Ansgar Jüngel, Tuấn Tùng Nguyến
wiley   +1 more source

The Linearized Inverse Boundary Value Problem in Strain Gradient Elasticity

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this paper we study the linearized version of the strain gradient elasticity equation in ℝ2$$ {\mathbb{R}}^2 $$ with constant coefficients and we prove that one can determine the two Lamé coefficients λ,μ$$ \lambda, \mu $$ as well as the internal strain gradient parameter g$$ g $$, as indicated by Mindlin in his revolutionary papers in 1963–
Antonios Katsampakos, Antonios Charalambopoulos   +1 more
wiley   +1 more source

Numerical Investigation of a Diffusive SIR Model: Focus on Positivity Preservation

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this paper, we consider a system of semilinear partial differential equations (PDEs) representing a spatially extended SIR epidemic model. A brief analytical investigation of the well‐posedness and positivity of the solutions is provided in the appendix, while the main focus is on the numerical treatment of the model.
Rahele Mosleh, Claudia Panico, Messoud Efendiyev   +2 more
wiley   +1 more source

The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains

Electronic Journal of Differential Equations, 2006
It is well-known that the Dirichlet problem for the Monge-Amp`ere equation $det D^2 u = mu$ in a bounded strictly convex domain $Omega$ in $mathbb{R}^n$ has a weak solution (in the sense of Aleksandrov) for any finite Borel measure $mu$ on $Omega$ and ...
David Hartenstine
doaj  

Wave equation with Dirichlet boundary conditions

, 2017
Partial differential equations derived from relationship between different physical and geometric problems where the function depends on two or more independent variables. Hyperbolic equations are a type of partial differential equations. In this paper, we consider the wave equation as a special form of hyperbolic equations.
Kocaleva, Mirjana, Zlatanovska, Biljana, Stojanova, Aleksandra, Stojkovic, Natasa, Gicev, Vlado   +4 more
openaire   +1 more source

Weak Solutions for a Class of Nonlocal Singular Problems Over the Nehari Manifold

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this paper, we consider a nonlocal model of dilatant non‐Newtonian fluid with a Dirichlet boundary condition. By using the Nehari manifold and fibering map methods, we obtain the existence of at least two weak solutions, with sign information.
Zhenfeng Zhang, Calogero Vetro, Tianqing An   +2 more
wiley   +1 more source

Linear Toroidal‐Inertial Waves on A Differentially Rotating Sphere with Application to Helioseismology: Modeling, Forward and Inverse Problems

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a fourth‐order scalar equation.
Tram Thi Ngoc Nguyen, Damien Fournier, Laurent Gizon, Thorsten Hohage   +3 more
wiley   +1 more source