This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes, e.g., wave-propagation or heat-transfer, that are modeled by wave equations or heat equations. Here, we study both parabolic and hyperbolic equations. We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods, which are standard splitting me...

This paper is concerned with linear parabolic partial diierential equations in divergence form and their discrete analogues. It is assumed that the coeecients of the equation are stationary random variables, random in both space and time. The Green's functions for the equations are then random variables. Regularity properties for expectation values of Green's functions are obtained. In particul...

In the so-called Spitzer-Härm regime, equations of plasma physics reduce to a non linear parabolic equation for the electronic temperature. Coming back to the derivation of this limiting equation through hydrodynamic regime arguments, one is led to construct a hierarchy of models where the heat fluxes are defined through a non-local relation which can be reinterpreted as well by introducing cou...

We study existence, uniqueness, and a priori estimates for solutions for backward parabolic Ito equations in domains with boundary. The proofs are based duality between forward and backward equations. This duality is used also to establish that backward parabolic equations have some causality (more precisely, some anti-causality). AMS 1991 subject classification: Primary 60J55, 60J60, 60H10. Se...

The aim of this research was manufacturing a parabolic trough solar collector in which reflecting surface is made of mirror steel rather than usual mirror and also predicting its theoretical performance.by adjusting planar ⩝ -shaped structures parallel to each other and welding them together, the main supporting structure was assembled and a parabolic-shape Teflon arc was installed in the apert...

in the present article, we focus on the numerical approximation of stochastic partial differential equations of itˆo type with space-time white noise process, in particular, parabolic equations. for each case of additive andmultiplicative noise, the numerical solution of stochastic diffusion equations is approximated using two stochastic finite difference schemes and the stability and consisten...

An initial-boundary value problem for 1D flow of a compressible viscous heat-conducting micropolar fluid is considered; the fluid is thermodynamically perfect and polytropic. Assuming that the initial data are Hölder continuous on 0, 1 and transforming the original problem into homogeneous one, we prove that the state function is Hölder continuous on 0, 1 × 0, T , for each T > 0. The proof is b...