Studies on blow-up

منو

" Studies on blow-up "
A. A. H. Saleh

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	1113377
Doc. No	:	TLpq230869259
Main Entry	:	A. A. H. Saleh
Title & Author	:	Studies on blow-up\ A. A. H. Saleh
College	:	King Fahd University of Petroleum and Minerals (Saudi Arabia)
Date	:	1994
student score	:	1994
Degree	:	M.S.
Page No	:	58
Abstract	:	It is known that the solution of the nonlinear reaction-diffusion equationusdusd\eqalign{ut &= \Delta u + u\sp\lambda\quad x \in R\sp{n},\ 1 3\cr u(0,x) &= u\sb9(x)\quad x\in R\sp{n}.}usdusdbecomes unbounded in finite time no matter how small the initial data usdu\sb0usd is. This time is known as the finite blow-up time. In this thesis, we push the blow-up time into infinity for the general equation by introducing a cooling term, that is the equation usdusd\eqalign{u\sb{t} &= \Delta u + f(u, x)- {2\vert\nabla u\vert\sp2\over(u + 1)}\quad x\in R\sp{n},\ t > 0\cr u(0,x) &= u\sb0(x)\quad x\in R\sp{n}}usdusdAlso, the infinite time blow-up of usdu(x,t)usd will occur at the infinity; usd\vert x\vert = \infty.\ R\sp{n}usd.
Subject	:	Mathematics
	:	Pure sciences