CAJ | 학술논문

考虑退化方程u_t=div(|▽u|~(p-2)▽u)+u~q的Cauchy问题,其中初始函数u_0(x)的支集有界,p>2,1<q<p-1,最大存在时间0＜T＜∞.用以研究带有热源项的支集边界的正则性;并通过构造逼近解序列的办法，利用比较原理证明了解u的自由边界关于空间变量x是Lipschitz连续的;进一步地, 如果对u_0(x)和非线性指标q做额外的假设,可以证明自由边界关于时间变量t也是局部Lipschitz连续的.
고필퇴화방정u_t=div(|▽u|~(p-2)▽u)+u~q적Cauchy문제,기중초시함수u_0(x)적지집유계,p>2,1<q<p-1,최대존재시간0＜T＜∞.용이연구대유열원항적지집변계적정칙성;병통과구조핍근해서렬적판법，이용비교원리증명료해u적자유변계관우공간변량x시Lipschitz련속적;진일보지, 여과대u_0(x)화비선성지표q주액외적가설,가이증명자유변계관우시간변량t야시국부Lipschitz련속적.
This paper is concerned with the Cauchy problem u_t=div(|▽u|~(p-2)▽u)+u~q,with initial u_0(x) has bounded compact support,p＞2,1＜q＜p-1,the most exist time 0＜T＜∞.This work establishes the regularity of the free boundary.By comparing with the constructed approximate sequence,the author proves that the boundary is Lip-continuous with space variables x,moreover,the boundary is local Lip-continuous with time variables t,provided that some assumptions on the initial data u_0 and q are made.