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Showing 1 to 20 of 34 for “"Dirichlet boundary conditions"”.
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Positive Symmetric Solutions Of A Boundary Value Problem With Dirichlet Boundary Conditions
… point theorem of function type to a second order boundary value problem with Dirichlet boundary conditions. We show the existence of positive symmetric solutions of this boundary value problem. </p>
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Applications Of Leggett Williams Type Fixed Point Theorems To A Second Order Difference Equation
… class of second-order difference equations with Dirichlet boundary conditions. We present these fixed point theorems and then show what conditions have to be met in order to satisfy the theorem. Finally, we provide specific examples to show the hypotheses of the theorems do not contradict one …
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SDEs and MFGs towards Machine Learning applications
… within a confined domain under the imposition of Dirichlet boundary conditions. The investigation culminates in exploring pertinent Machine Learning methodologies applied to financial and economic decision-making processes.
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Numerical approximations of coupled forward-backward SPDEs with applications
… equations (FBSPDEs) with homogeneous Dirichlet boundary conditions. For the FBSPDE, the finite element method in the spatial domain leads to approximations by finite-dimensional forward-backward stochastic differential equations (FBSDEs) in the temporal domain. We then approximate the …
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Vague convergence of spectral shift functions for periodic restrictions of one-dimensional Schrodinger operators
… of the form $(-\ell,\ell)$ with periodic boundary conditions to the full-line spectral shift function in the infinite volume limit $\ell\to \infty$. The approach employed relies on the use of a Krein-type resolvent identity to relate the resolvent of the operator with periodic boundary …
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Blow-up of Solutions to the Generalized Inviscid Proudman-Johnson Equation
… equation endowed with periodic or Dirichlet boundary conditions. More particularly,regularity of solutions in an Lp setting will be measured via a direct approach which involves the derivation of representation formulae for solutions to the problem. For a real parameter lambda, …
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Neumann Solutions to a Two-Phase Elliptic Free Boundary Problem in R^2
… We require admissible functions to satisfy Dirichlet boundary conditions on a portion of the fixed boundary with positive one-dimensional Hausdorff measure and Neumann boundary conditions on the rest of the fixed boundary. In this thesis we consider the behavior of minimizers in a …
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Distributed Parameter Control of Thermal Fluids
… heat equations. The control is applied through Dirichlet boundary conditions. We concentrate on a two-dimensional mode and use a semidiscrete Galerkin scheme for numerical computations. We construct both a linear control and a non-linear quadratic control and apply them to the full non-linear …
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Optimal design problems for quasidisks and partially clamped drums: Existence, symmetrization, and numerical methods
… each eigenvalue of the Laplacian, subject to Dirichlet boundary conditions, attains its extrema over each of these classes. The design problem of extremizing the fundamental tone of a drum fastened only on a fraction of the boundary is considered. The special case of minimizing the fundamental …
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Patterns in an elastic bar
… x is an element of the set (0, 1). with double Dirichlet boundary conditions. Here the potential W(p) = ((|p| - 1)²), is not differentiable at p = 0.;We define and prove existence and uniqueness of periodic solutions with any number n ≥ 0 of internal zeroes for all ɑ, γ > 0 and discuss the …
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Unstructured surface and volume decimation of tessellated domains
… The decimation algorithm enforces Dirichlet boundary conditions, uses only existing vertices, and assumes manifold geometry. Local dynamic vertex removal is performed without history information while preserving the initial topology and boundary geometry. The tessellation at each …
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Modeling Non-Rotational Ocean Circulation and Heat Distribution in Icy Moons
… thermal conductivity and fixed Dirichlet boundary conditions, initialized with a linear temperature gradient from −10 K at the surface to +10 K at the base. Over 1000 time steps, the temperature profile became nonlinear, with a kink indicating the transition from ice to water. …
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Rapid Implicit Diagonalization of Variable-Coefficient Differential Operators Using the Uncertainty Principle
… PDEs (second-order, one space dimension, Dirichlet boundary conditions) that can be used to obtain more accurate and reliable solutions than traditional methods. Previously, it was shown that conventional time-stepping methods could be avoided for time-dependent mathematical models …
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Use of Improved Far -Field Boundary Conditions to Compute External Flows on Reduced Domains
… to computations using Neumann and free-stream Dirichlet boundary conditions.
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Fast Marching Methods - parallel implementation and analysis
… as partial differential equations with Dirichlet boundary conditions, called Eikonal equation: $F(x)|\nabla T(x)|=1$, for $x \in \Omega$ and $T(x)=0$ for $x \in \Gamma$, where $\Omega$ is a domain in $\mathbb{R}^n$, $\Gamma$ is the initial position of a curve evolving with normal …
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pQCD energy loss and thermal field theory in small systems
… that has been geometrically confined by means of Dirichlet boundary conditions. This toy model reveals, via thermal field theoretic techniques, that quantum fields are very sensitive to the presence of a boundary, presenting significant deviations from the Stefan-Boltzmann limit and revealing a …
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Approximations and Object-Oriented Implementation for a Parabolic Partial Differential Equation
… a numerical study of the 2-D heat equation with Dirichlet boundary conditions over a polygonal domain. The motivation for this study is a chemical vapor deposition (CVD) reactor in which a substrate is heated while being exposed to a gas containing precursor molecules. The interaction between the …
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Hybrid atomistic-continuum formulations for gaseous flows
… coupling method and the imposition of continuum boundary conditions on the atomistic subdomain. The relative merits of different approaches for both are delineated and demonstrated using sample test problems. For the case of incompressible steady gaseous flows a hybrid formulation is developed …
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Singularly nonautonomous semilinear evolution equations with almost sectorial operators
… equations: one with Neumann homogeneous boundary condition in and another with nonhomogeneous and time-dependent Dirichlet boundary conditions in R0. The properties of those two decoupled equations are thoughtfully studied and from them, estimates on the pullback attractor are obtained.
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A Finite-Element Coarse-GridProjection Method for Incompressible Flows
… validated on standard test cases with realistic boundary conditions using unstructured triangular meshes. We also pioneer investigations of the effects of CGP on the accuracy of the pressure field. It is found that although CGP reduces the pressure field accuracy, it preserves the accuracy of the …
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