THE HEAT EQUATION WITH A SINGULAR POTENTIAL
THE HEAT EQUATION WITH A SINGULAR POTENTIAL
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DOI：
10.1090/s0002-9947-1984-0742415-3
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发表时间：
1984
影响因子：
1.3
通讯作者：
P. Baras;J. Goldstein
中科院分区：
文献类型：
--
作者：
P. Baras;J. Goldstein
令人关注的是单一问题$\frac{du}{dt}=au +\frac{c}{|x|^2}iz + f((,x),t$，$z(x,0)=u_0(x)$及其推广形式。在此，$c>0$，$x\in\mathbb{R}^N$，$t>0$，并且$f$和$u_0$是非负的且两者不全恒为零。存在一个与维度相关的常数$C(N)$，使得当$c>C_N$时问题无解。对于$c\leq C_N$，找到了$f$和$u_0$使得存在非负解的充分必要条件。
Of concern is the singular problem du/dt = au + (c/|x|2)iz + /((, x), tz(x,0) = u0(x), and its generalizations. Here c > 0, x G RN, t > 0, and/and t/0 are nonnegative and not both identically zero. There is a dimension dependent constant C (N) such that the problem has no solution for c> Ct(N). For c =S Ct(A/) necessary and sufficient conditions are found for / and u0 so that a nonnegative solution exists.