Source-Type Solutions Of Several Classes Of Parabolic Equations

This paper investigates source-type solutions of several classes of parabolic equations. The source-type solutions of second-order parabolic equations and high-order parabolic equations are both studied. On the problem of the source-type solutions of second-order parabolic equations, we discuss source-type solutions of the Cauchy problem ut =Δφ(u ) ? f (u ). During the study process, first research is on the existence and nonexistence as well as a very singular solution of the souce-type of the porous media equation with absorption (whichφ(u ) = u m , f (u )= up). Second research is on existence and nonexistence as well as a very singular solution of source-typy solution of degenerate quasilinear parabolic equations (whichφ( s )∈C [0,∞)∩C1(0,∞),φ(0) = 0.). On source-type solutions of high-order parabolic equations, first research is on qualitative properties of selfsimilar source solutions of a fourth order degenerate parabolic equation ht = ? ( h n hx xx ) x + c ( hm)xx,as well as existence and asymptotic behaviour of souce-type of parabolic equation when c = 1 and c = ?1 . Second research is on existence, nonexistence, asymptotic behaviour, uniqueness and an explicit solution of source-type solution of a fourth order nonliner degenerate papabolic equation ut = ? (| u |n uxxx )x.We have carried out detailed analysis and rigorous proof on every question of the proposed in this thsis. Some of them are the result of a number of documents with the extension of the promotion. This study further discussion of the parabolic equation-oriented solutions has a certain significance.