延边大学学报(自然科学版)
延邊大學學報(自然科學版)
연변대학학보(자연과학판)
JOURNAL OF YANBIAN UNIVERSITY(NATURAL SCIENCE EDITION)
2002年
4期
241-246
,共6页
自型解%半线性抛物方程%存在性和唯一性
自型解%半線性拋物方程%存在性和唯一性
자형해%반선성포물방정%존재성화유일성
Self-similar solution%Semilinear parabolic equation%Existence and uniqueness
研究了拟线性抛物型方程ut=uxx-|u|p-1u的前向自型解.通过构造半线性微分方程的径向解,证明了自型解的存在性和唯一性.
研究瞭擬線性拋物型方程ut=uxx-|u|p-1u的前嚮自型解.通過構造半線性微分方程的徑嚮解,證明瞭自型解的存在性和唯一性.
연구료의선성포물형방정ut=uxx-|u|p-1u적전향자형해.통과구조반선성미분방정적경향해,증명료자형해적존재성화유일성.
We investigate the structure of radial solutions of a semilinear equation f" + r/2f +1/p - 1f - | f | p-1f = 0, r ＞ 0, which is related to forward self-semilar solutions of a semilinear parabolic equation ut = uxx-| u | p-1u defined in the upper half planeQ = {(x,t) | x ∈ R,t ＞ 0}, where 1 ＜ p ＜ 3. We study the existence, uniqueness, and parameter dependency of rapidly decaying solutions with a prescribed number of zeros.
