Selfsimilar Solutions of the Second Kind for the Modified Porous Medium Equation
نویسندگان
چکیده
We construct compactly supported self-similar solutions of the Modi ed PorousMedium Equation (MPME) ut = um for um > 0 (1 + ") um for um < 0: They have the form u(x; t) = t U(x t ); where the similarity exponents and depend on ", m and the dimension N . This corresponds to what is known in the literature as anomalous exponents or self-similarity of the second kind, a not completely understood phenomenon. This paper performs a detailed study of the properties of the anomalous exponents of the MPME.
منابع مشابه
Maximal Viscosity Solutions of the Modified Porous Medium Equation
We construct a theory for maximal viscosity solutions of the Cauchy problem for the modiied porous medium equation u t + ju t j = (u m), with 2 (?1; 1) and m > 1. We investigate the existence, uniqueness, nite propagation and optimal regularity of these solutions. As a second main theme we prove that the asymptotic behaviour is given by a certain family of self-similar solutions of the so-calle...
متن کاملNonlocal porous medium equation: Barenblatt profiles and other weak solutions
A degenerate nonlinear nonlocal evolution equation is considered; it can be understood as a porous medium equation whose pressure law is nonlinear and nonlocal. We show the existence of sign changing weak solutions to the corresponding Cauchy problem. Moreover, we construct explicit compactly supported selfsimilar solutions which generalize Barenblatt profiles — the well-known solutions of the ...
متن کاملTraveling Wave Solutions of 3D Fractionalized MHD Newtonian Fluid in Porous Medium with Heat Transfer
In the present paper, we get exact solutions of Magnetohydrodynamic (MHD) of the fractionalized three-dimensional flow of Newtonian fluid with porous and heat transfer through the traveling wave parameter. The governing equations are produced dependent on established Navier-stokes equations which can be diminished to ordinary differential equation by wave parameter ξ=ax+by+nz+Utα/Γ(α...
متن کاملThree-dimensional analytical models for time-dependent coefficients through uniform and varying plane input source in semi-infinite adsorbing porous media.
In the present study, analytical solutions are developed for three-dimensional advection-dispersion equation (ADE) in semi-infinite adsorbing saturated homogeneous porous medium with time dependent dispersion coefficient. It means porosity of the medium is filled with single fluid(water). Dispersion coefficient is considered proportional to seepage velocity while adsorption coefficient inversel...
متن کاملThree-dimensional analytical models for time-dependent coefficients through uniform and varying plane input source in semi-infinite adsorbing porous media.
In the present study, analytical solutions are developed for three-dimensional advection-dispersion equation (ADE) in semi-infinite adsorbing saturated homogeneous porous medium with time dependent dispersion coefficient. It means porosity of the medium is filled with single fluid(water). Dispersion coefficient is considered proportional to seepage velocity while adsorption coefficient inversel...
متن کاملذخیره 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 2007