一類多維非線性拋物方程解的存在性與Blow-up.pdf

1、Y12i1966分婁號(hào)UDC密級(jí)編號(hào)理學(xué)碩士學(xué)位論文一類多維非線性拋物方程解的存在性與Blow—up碩士研究生指導(dǎo)教師學(xué)科、專業(yè)李寶平劉亞成教授應(yīng)用數(shù)學(xué)哈爾濱工程大學(xué)2007年4月哈爾濱_『稃大學(xué)碩十學(xué)位論文AbstractInthispaper，weconsidertheinitialboundaryvalueproblemforaclassofmultidimensionalnonlinearparabolicequation虬一A

2、u，=∑or，(‰)‘V(“)，工∈Q，，0(1)I=l材I，。o=UO(x)，x∈f2，t0(2)“l(fā)∞=0，t0(3)QcR”isapropriateboundeddomainand廠∈CAndtheexistenceofsolutionisestablishedWhen盯，0)(1≤i≤療)，廠似)satisfy(H1)or，，f∈C，3k，satisfy參(s)=盯，(s)一ks一盯，(0)isnotdecreasingfunc

3、tion。(日2)刊，AiandOro，satisfyAi阿≤協(xié)(j)l≤Alsl。(日3)3B，Biand，，satisfyI廠(“)I≤8117Bwhere1≤y4七，A，AI，B，BIand口，，areconstant，weobtaintheexistenceanduniquene—SSoftheglobalgeneralizedsolutionWhenOr：(s)Osis療)，廠’(U)arebonudedthereexists

4、auniqueglobalstrongsolutionThenormegativityofthesolutioncorrespondingtothenonnegativeinitialboundaryvalue，theasymptoticbehaviorandtheblowupofthesolutionarealsodiscussedForthecaseoforledimension，moregeneralboundaryconditi