Mathematical results are presented that strongly constrain the prototypification of complex shape. Such shape requires local prototypification in two senses: (1) prototypification occurs in parallel at different parts of the figure, and (2) prototypification varies diferentially (smoothly) across an individual part. With respect to (l), we present a theorem that states that every Hoffman-Richar...

[1] This paper presents a class of analytical solutions for transient flow into unsaturated rock matrix. These analytical solutions are derived using specially correlated, physically meaningful relative permeability and capillary functions. The transient flow processes in unsaturated rock matrix blocks are generally described by the Richards’ equation. The analytical solutions describe the full...

We address a problem of boundary control for nonlinear scalar conservation law. Namely, this article is devoted to the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) with triangular flux function evolving along single road. The target state time- and space-dependent trajectory. law constructed using analytical solution Hamilton–Jacobi (H–J) equation, which an integral form...

In this paper, a new nonlinear heat equation is studied that arises as model of the collective behavior automated vehicles. The properties solutions are by introducing appropriate notion weak solution requires certain entropy-like conditions. To obtain an approximation equation, conservative first-order finite difference scheme proposed respects corresponding entropy conditions, and links betwe...

How to estimate queue length in real-time at signalized intersection is a long-standing problem. The problem gets even more difficult when signal links are congested. The traditional input–output approach for queue length estimation can only handle queues that are shorter than the distance between vehicle detector and intersection stop line, because cumulative vehicle count for arrival traffic ...

Pseudoparabolic equations in periodic media are homogenized to obtain upscaled limits by asymptotic expansions and two-scale convergence. The limit is characterized and convergence is established in various linear cases for both the classical binary medium model and the highly heterogeneous case. The limit of vanishing time-delay parameter in either medium is included. The double-porosity limit...

A recent approach to solve Richards' equation is further improved. This approach brings understanding into the physical processes of in®ltration and ponding. In particular we apply it to analyze the standard hydrologic tool of Time Compression Approximation (TCA). We also suggest that the new approach provides a more reliable alternative to TCA, e.g. for predicting ponding time. Ó 1999 Elsevier...

In this paper, we study about the problem of stationary infiltration on several types homogeneous soil from a single trapezoidal channel. A governing equation in is form nonlinear differential and called Richards’ equation. The can be solved more easily by transforming it into modified Helmholtz study, Dual Reciprocity Boundary Element Method (DRBEM) was used to solve numerically. Then, using o...