Periodic solutions for a porous medium equation
نویسندگان
چکیده
منابع مشابه
Periodic solutions of a porous medium equation
In this paper, we study with a periodic porous medium equation with nonlinear convection terms and weakly nonlinear sources under Dirichlet boundary conditions. Based on the theory of Leray-Shauder fixed point theorem, we establish the existence of periodic solutions.
متن کاملProbabilistic approximation for a porous medium equation
In this paper, we are interested in the one-dimensional porous medium equation when the initial condition is the distribution function of a probability measure. We associate a nonlinear martingale problem with it. After proving uniqueness for the martingale problem, we show existence owing to a propagation of chaos result for a system of weakly interacting di usion processes. The particle syste...
متن کاملMaximal 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 کاملPerron’s Method for the Porous Medium Equation
This work extends Perron’s method for the porous medium equation in the slow diffusion case. The main result shows that nonnegative continuous boundary functions are resolutive in a general cylindrical domain.
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: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2011
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2011.1.42