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1.
Joanna M. Goard Philip Broadbridge Daniel J. Arrigo 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1996,47(6):926-942
The nonlinear diffusion equationu
t=[f(u)g(u
x
)] arises in recent models of turbulent transport and of stress dissipation in rock blasting. A Lie point symmetry analysis produces many similarity reductions of exponential and power-law forms, and reveals that for all choices off the equation is always integrable wheng(u
x
)=1/u
x
. We identify the functionsf(u) which guarantee equivalence to the linear heat equation. For all other choices off, the linear canonical form leads to a self-adjoint differential equation by separation of variablesx andt. We construct a number of explicit solutions with simple boundary conditions, which illustrate behavior in the vicinity of the degenerate region withu
x
=. If zero flux and constant concentration are maintained on free boundaries, then steep concentration gradients may evolve from smooth initial conditions. For other boundary conditions, unlike the examples of strong degeneracy, smoothing will occur at initial step discontinuities. 相似文献
2.
It is shown that the determining equations for generalised conditional symmetries (GCSs) of order n, of an evolution equation of arbitrary order, can be found as a consequence of compatibility with an nth-order invariant surface condition. The compatibility technique is demonstrated on a second-order nonlinear diffusion–convection equation with absorption and used to find new GCSs of a linear diffusion equation with nonlinear source. 相似文献
3.
H. v. Euler C. Zimmerlund C. van der Hoeven R. Riwlin A. Fodor A. K. Goard J. Effront F. König P. Surun J. M. Kolthoff A. S. Coolidge W. Bachmann L. Maier O. Wolff J. E. Teeple und P. Mahler 《Fresenius' Journal of Analytical Chemistry》1929,78(7-8):297-304
Ohne Zusammenfassung 相似文献
4.
J. Goard 《Journal of Nonlinear Mathematical Physics》2019,26(3):327-332
In this note we prove that the method of Bîlã and Niesen to determine nonclassical determining equations is equivalent to that of Nucci’s method with heir-equations and thus in general is equivalent to using an appropriate form of generalised conditional symmetry. 相似文献
5.
Goard M Aakalu G Fedoryak OD Quinonez C St Julien J Poteet SJ Schuman EM Dore TM 《Chemistry & biology》2005,12(6):685-693
The regulation of protein synthesis is vital for a host of cell biological processes, but investigating roles for protein synthesis have been hindered by the inability to selectively interfere with it. To inhibit protein synthesis with spatial and temporal control, we have developed a photo-releasable anisomycin compound, N-([6-bromo-7-hydroxycoumarin-4-yl]methyloxycarbonyl)anisomycin (Bhc-Aniso), that can be removed through exposure to UV light. The area of protein synthesis inhibition can be restricted to a small light-exposed region or, potentially, the volume of two-photon excitation if a pulsed IR laser is the light source. We have tested the compound's effectiveness with an in vitro protein-translation system, CHO cells, HEK293 cells, and neurons. The photo-released anisomycin can inhibit protein synthesis in a spatially restricted manner, which will enable the specific inhibition of protein synthesis in subsets of cells with temporal and spatial precision. 相似文献
6.
7.
Joanna Goard 《Applicable analysis》2013,92(5):473-481
It is generally believed that in order to solve initial and boundary value problems using Lie symmetry methods, the boundary and initial conditions need to be left invariant by the infinitesimal symmetry generator which admits the invariant solution. In this article we give less restrictive conditions on the imposed initial and boundary values in order that they be recoverable with a particular symmetry generator. 相似文献
8.
9.
Philip Broadbridge Joanna M. Goard 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(3):534-538
An exact solution is given for the evolution of an
initially v-shaped surface by a fully nonlinear diffusion
equation. This is the unique generalized solution that is
continuous but not twice differentiable. Since the profile
velocity decreases faster than the reciprocal of the profile
curvature, the point of infinite curvature persists for a finite
positive time. 相似文献
10.
The coefficients in the stochastic differential equation that the short interest rate follows are of vital importance in the subsequent modelling of bond prices and other interest rate products. Empirical tests have previously been performed by various authors who compare a variety of popular short‐rate models. Most recently, Ahn and Gao compared their model with affine‐drift models and showed that their model with a non‐linear drift function outperforms the others. This paper compares the model developed by Goard, which is a time‐dependent generalization of the Ahn–Gao model, with the Ahn–Gao model itself. It is found that the time‐dependent model using a second‐order Fourier series in time, outperforms the Ahn–Gao model for all data sets considered. 相似文献