Homogeneous solutions of the generalized heat equation
نویسندگان
چکیده
منابع مشابه
Exact Solutions of the Generalized Kuramoto-Sivashinsky Equation
In this paper we obtain exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems. The methods used to determine the exact solutions of the underlying equation are the Lie group analysis and the simplest equation method. The solutions obtained are then plotted.
متن کاملMinimal Solutions of the Heat Equation and Uniqueness of the Positive Cauchy Problem on Homogeneous Spaces
The minimal positive solutions of the heat equation on A' X (-00, 7") are determined for X a homogeneous Riemannian space. A simple proof of uniqueness for the positive Cauchy problem on a homogeneous space is given using Choquet's theorem and the explicit form of these solutions. Introduction. A minimal solution of a linear elliptic or parabolic equation is a nonnegative solution u such that, ...
متن کاملUnbounded solutions of the nonlocal heat equation
We consider the Cauchy problem posed in the whole space for the following nonlocal heat equation: ut = J ∗u−u , where J is a symmetric continuous probability density. Depending on the tail of J , we give a rather complete picture of the problem in optimal classes of data by: (i) estimating the initial trace of (possibly unbounded) solutions; (ii) showing existence and uniqueness results in a su...
متن کاملNon homogeneous Heat Equation : Identi cation
We study the nonhogeneous heat equation under the form: u t ? u xx = '(t)f(x), where the unknown is the pair of functions (u; f). Under various assumptions about the the function ' and the nal value in t = 1 i.e. g(x), we propose diierent regularizations on this ill-posed problem based on the Fourier transform associated with a Lebesgue measure. For ' 6 6 0 the solution is unique. I. Introducti...
متن کاملHomogeneous generalized master equation retaining initial correlations
Using the projection operator technique, the exact homogeneous generalized master equation (HGME) for the relevant part of a distribution function (statistical operator) is derived. The exact (mass) operator governing the evolution of the relevant part of a distribution function and comprising arbitrary initial correlations is found. Neither the Bogolyubov principle of weakening of initial corr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1997
ISSN: 0263-6115
DOI: 10.1017/s1446788700000537