Weak solutions of the porous medium equation

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Nonlocal 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 کامل

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 کامل

Regularity of weak solutions of the Cauchy problem to a fractional porous medium equation

This paper concerns the regularity of the weak solutions of the Cauchy problem to a fractional porous medium equation with a forcing term. In the recent work (Fan et al. in Comput. Math. Appl. 67:145-150, 2014), the authors established the existence of the weak solution and the uniqueness of the weak energy solution. In this paper, we show that the every nonnegative bounded weak energy solution...

متن کامل

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 کامل

Perron’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 کامل

ذخیره 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: Transactions of the American Mathematical Society

سال: 1993

ISSN: 0002-9947,1088-6850

DOI: 10.1090/s0002-9947-1993-1085939-x