论文标题
罗宾边界条件的杆上的温度
Temperature on rods with Robin boundary conditions
论文作者
论文摘要
我们将解决方案$ u_f $考虑到l^1 [-π，π] $中的一维知更蛋白问题$ f \ 和Robin参数$α> 0 $。对于给定的$ m $，$ m $和$ s $， $ 0 \ le m <s <m $，我们确定热源 $ f_0 $，因此$ u_ {f_0} $最大化温度差距 $ \ max _ {[ - π，π]} u_f - \ min _ {[ - π，π]} u_f $在所有热量上 来源$ f $，使得$ m \ le f \ le m $和$ \ | f \ | _ {l^1} =2πs$。在 特别是，这回答了J.〜J.〜Langford和P.〜McDonald在\ Cite {LM}中提出的一个问题。我们还确定了在给定点$ x_0 \ in [-π，π] $在同一类热源上的热源上最大化/最小化$ u_f $的热源，并讨论了一些相关的问题。
We consider solutions $u_f$ to the one-dimensional Robin problem with the heat source $f\in L^1[-π,π]$ and Robin parameter $α>0$. For given $m$, $M$, and $s$, $0\le m<s<M$, we identify the heat sources $f_0$, such that $u_{f_0}$ maximizes the temperature gap $\max_{[-π,π]}u_f -\min_{[-π,π]}u_f$ over all heat sources $f$ such that $m\le f\le M$ and $\|f\|_{L^1}=2πs$. In particular, this answers a question raised by J.~J.~Langford and P.~McDonald in \cite{LM}. We also identify heat sources, which maximize/minimize $u_f$ at a given point $x_0\in [-π,π]$ over the same class of heat sources as above and discuss a few related questions.
