一类非线性双曲抛物方程熵解的稳定性  

Stability of Entropy Solution to the Cauchy Problem for a Nonlinear Hyperbolic-Parabolic Equation

作　　者：陈淑琴[1] 詹华税[1] 

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《集美大学学报（自然科学版）》2011年第4期306-310,共5页Journal of Jimei University：Natural Science

基　　金：福建省自然科学基金资助项目(2009J01009);集美大学潘金龙科研基金资助项目(C510071)

摘　　要：考虑抛物-双曲方程:ut+a(x,t)/2.▽xu2=Δu+,t>0,其中a是向量值函数,diva≤0,且u+=max{u,0}.该方程在[u<0]上是双曲方程,在[u>0]上是抛物方程.证明了若该方程的熵解在x→∞时不超过线性增长,那么它在加权的空间中解具有稳定性.同时,说明了线性增长条件对于它的解的唯一性成立时已经是最优化的条件了.The cauehy problem for a nonlinear hyperbolic-parabolic equation u2 ＋ a（x,t）/2 ·▽xu^2 = Au＋, for t 〉 O（ ＊ ） was considered, where a was a variable vector, div a ≤〈 0 , and u＋ = max { u,O } . The equation was hyperbolic equation in the region [ u 〈 0 ] and parabolic in the region [ u 〉 0 ] . It was shown that entropy solution to the equation that grew at most linearly as x →∞ was stable in a weighted L1 （RN） space, which implied that the solutions were unique. The linear growth as x→∞imposed on the solution was shown to be optimal for uniqueness to hold.

关 键 词：稳定性 熵解 双曲-抛物方程 

分 类 号：O175.29[理学—数学]