Nonlinear diffusion in an inhomogeneous aquifer

نویسندگان

  • M. Guedda
  • D. Hilhorst
  • M. A. Peletier
چکیده

A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract We study the large-time behaviour and the behaviour of the interfaces of the nonlinear diiusion equation (x)u t = A(u) in one and two space dimensions. The function A is of porous media type, smooth but with a vanishing derivative at some values of u, and > 0 is supposed continuous and bounded from above. If is not bounded away from zero, the large-time behaviour of solutions and their interfaces can be essentially diierent from the case when is constant. We extend results by Kamin and Rosenau ((13], 14]) and derive the large-time asymptotic behaviour of solutions, as well as a precise characterisation of the behaviour of the interfaces of solutions in one space dimension and in some cases in two space dimensions. In one space dimension and when is monotonic the result states that the interface (t) = supfx 2 R : u(x; t) > 0g tends to innnity in nite time if and only if R 1 0 xx(x) dx < 1.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A robust and efficient method for steady state patterns in reaction-diffusion systems

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton's method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, ...

متن کامل

J an 1 99 8 CHAOS AND ENERGY REDISTRIBUTION IN THE NONLINEAR INTERACTION OF TWO SPATIO - TEMPORAL WAVE TRIPLETS ∗

In this paper we examine the spatio-temporal dynamics of two nonlinearly coupled wave triplets sharing two common modes. Our basic findings are the following. When spatial dependence is absent, the homogeneous manifold so obtained can be chaotic or regular. If chaotic, it drives energy diffusion from long to small wavelengths as soon as inhomogeneous perturbations are added to the system. If re...

متن کامل

Existence and Nonexistence of Global Solutions in Time for a Reaction-Diffusion System with Inhomogeneous Terms

We consider the initial value problem for the reaction-diffusion system with inhomogeneous terms. In this paper we show the existence and nonexistence of global solution in time. Especially, for the nonexistence we extend the conditions of the nonlinear terms and the initial data to the weaker conditions. We prove that for the nonlinear term and the initial data whose support is included in som...

متن کامل

AN ANALYTICAL SOLUTION FOR DIFFUSION AND NONLINEAR UPTAKE OF OXYGEN IN THE RETINA

A simple mathematical model of steady state  oxygen distribution subject to diffusive transport and non- linear uptake in a retinal cylinder has been developed. The approximate analytical solution to a reaction- diffusion equation are obtained by using series expansions. The computational results for the scaled variables are presented through graphs. The effect of the important parameters (1) d...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1995