Cauchy–Gelfand problem for quasilinear conservation law

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

The Conservation Law

Tensorial conservation law for nematic polymers.

We derive the "conservation law" for nematic polymers in tensorial form valid for quadrupolar orientational order, in contradistinction to the conservation law in the case of polar orientational order. Due to microscopic differences in the coupling between the orientational field deformations and the density variations for polar and quadrupolar order, we find that the respective order parameter...

Conservation law for self-paced movements.

Optimal control models of biological movements introduce external task factors to specify the pace of movements. Here, we present the dual to the principle of optimality based on a conserved quantity, called "drive," that represents the influence of internal motivation level on movement pace. Optimal control and drive conservation provide equivalent descriptions for the regularities observed wi...

A Ow Conservation Law for Surface Processes

The object studied in this paper is a pair ((; Y), where is a random surface in I R N and Y random vector eld on I R N. The pair is jointly stationary, i.e. its distribution is invariant under translations. The vector eld Y is smooth outside but may have discontinuities on. Gauss' divergence theorem is applied to derive a ow conservation law for Y. For I R 1 this specializes to a well-known rat...