Methods used in parabolic refraction-diiraction models for computing the evolution of monochromatic waves in the nearshore zone are used to construct a model for spectral wave conditions. The two dimensional spectrum is divided into discrete wave components and the individual wave components are computed simultaneously in the domain using parabolic models for each wave component. Statistical qu...

It is widely believed that if monotone difference schemes are applied to the linear convection equation with discontinuous initial data, then solutions of the monotone schemes are closer to solutions of their parabolic modified equations than that of the original convection equation. We will confirm the conjecture in this paper. It is well known that solutions of the monotone schemes and their ...

In this paper, we consider a stabilization problem for a fluid flow. For a perturbation of the velocity of an incoming flow on a flat plate, the laminar-to-turbulent transition location varies. We want to stabilize it by a suction velocity trough the plate. The linearization of the nonlinear model around a steady state solution leads to a linear degenerate parabolic equation. We look for a suct...

the release rate of potassium (k) from micaceous minerals plays a significant role in supplying k to plants. the objective of this study was to determine the most appropriate kinetic equation to describe potassium release from micaceous minerals as influenced by organic acids. muscovite and phlogopite were made to react with 0, 500, 2000 and 4000 ?m solutions of oxalic, citric and malic acids f...

A convergence proof is given for an abstract parabolic equation using general space decomposition techniques. The space decomposition technique may be a domain decomposition method, a multilevel method, or a multigrid method. It is shown that if the Euler or Crank-Nicolson scheme is used for the parabolic equation, then by suitably choosing the space decomposition, only O(jlog j) steps of itera...

We prove a difference equation analogue of the decay-of-mass result for the nonlinear parabolic equation ut = ∆u+ μ|∇u| when μ < 0, and a new growth result when μ > 0.

An adiabatic mode time-dependent parabolic equation for the 3D problems of underwater acoustic propagation problem is derived by the multiple-scale method. The Cauchy problem for this equation is considered.

in this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. in the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations.  also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. error estimates were also obtaine...

The minimal positive solutions of the heat equation on A' X (-00, 7") are determined for X a homogeneous Riemannian space. A simple proof of uniqueness for the positive Cauchy problem on a homogeneous space is given using Choquet's theorem and the explicit form of these solutions. Introduction. A minimal solution of a linear elliptic or parabolic equation is a nonnegative solution u such that, ...