Search results for " equations"
showing 10 items of 783 documents
The exact finite‐difference scheme for vector boundary‐value problems with piece‐wise constant coefficients
1998
We will consider the exact finite‐difference scheme for solving the system of differential equations of second order with piece‐wise constant coefficients. It is well‐known, that the presence of large parameters at first order derivatives or small parameters at second order derivatives in the system of hydrodynamics and magnetohydrodynamics (MHD) equations (large Reynolds, Hartmann and others numbers) causes additional difficulties for the applications of general classical numerical methods. Thus, important to work out special methods of solution, the so‐called uniform converging computational methods. This gives a basis for the development of special monotone finite vector‐difference schem…
Ambit processes and stochastic partial differential equations
2011
Ambit processes are general stochastic processes based on stochastic integrals with respect to Levy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Levy noise analysis.
A Parametric Dirichlet Problem for Systems of Quasilinear Elliptic Equations With Gradient Dependence
2016
The aim of this article is to study the Dirichlet boundary value problem for systems of equations involving the (pi, qi) -Laplacian operators and parameters μi≥0 (i = 1,2) in the principal part. Another main point is that the nonlinearities in the reaction terms are allowed to depend on both the solution and its gradient. We prove results ensuring existence, uniqueness, and asymptotic behavior with respect to the parameters.
Fixed Point Theorems in Partially Ordered Metric Spaces and Existence Results for Integral Equations
2012
We derive some new coincidence and common fixed point theorems for self-mappings satisfying a generalized contractive condition in partially ordered metric spaces. As applications of the presented theorems, we obtain fixed point results for generalized contraction of integral type and we prove an existence theorem for solutions of a system of integral equations.
Fronts propagating with signal dependent speed in limited diffusion and related Hamilton-Jacobi formulations
2021
We consider a class of limited diffusion equations and explore the formation of diffusion fronts as the result of a combination of diffusive and hyperbolic transport. We analyze a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion coefficient that depends on the unknown and on the gradient of the unknown. We explore the main features of the solution of the Hamilton-Jacobi equations that contain shocks and propose a suitable numerical scheme that approximates the solution in a consistent way with respect to the solution of the associated Fokker-Planck equation. We analyze three model problems covering d…
Convergence Theorems for Varying Measures Under Convexity Conditions and Applications
2022
AbstractIn this paper, convergence theorems involving convex inequalities of Copson’s type (less restrictive than monotonicity assumptions) are given for varying measures, when imposing convexity conditions on the integrable functions or on the measures. Consequently, a continuous dependence result for a wide class of differential equations with many interesting applications, namely measure differential equations (including Stieltjes differential equations, generalized differential problems, impulsive differential equations with finitely or countably many impulses and also dynamic equations on time scales) is provided.
Free-surface flows solved by means of SPH schemes with numerical diffusive terms
2010
A novel system of equations has been defined which contains diffusive terms in both the continuity and energy equations and, at the leading order, coincides with a standard weakly-compressible SPH scheme with artificial viscosity. A proper state equation is used to associate the internal energy variation to the pressure field and to increase the speed of sound when strong deformations/compressions of the fluid occur. The increase of the sound speed is associated to the shortening of the time integration step and, therefore, allows a larger accuracy during both breaking and impact events. Moreover, the diffusive terms allows reducing the high frequency numerical acoustic noise and smoothing …
Convex functions on Carnot Groups
2007
We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point of view is based on thinking of convex functions as subsolutions of homogeneous elliptic equations.
The body-mind problem from a personality relativity theory approach: (Relativity of personality)
2012
The body-mind problem is here posed fromthe General Factor of Personality Theory and mathematically presented as a relativity theory: 1. A two-level-invariant model; 2. The transformation equation between both levels. On a hand, the investigation of personality dynamicsas a consequenceof a stimulant drug provides a system of two coupled differential equations, which adapts to both biological (body) and psychological (mind)levels ofdescription. On the other hand, a system of two coupled partial differential equations is here deduced as the transformation model between the biological and psychological levels. Both models are presented and validated in this paper. The experimental design to va…
H2 O, H2 , HF, F2 and F2 O nuclear magnetic shielding constants and indirect nuclear spin-spin coupling constants (SSCCs) in the BHandH/pcJ-n and BHa…
2009
Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H(2)O, H(2), HF, F(2) and F(2)O nuclear isotropic shielding constants in the BHandH Kohn-Sham basis set limit was shown. The results of two- and three-parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization-consistent basis sets pcS-n and pcJ-n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were mor…