A NOTE ON THE BOUNDEDNESS OF SOLUTIONS OF LINEAR PARABOLIC EQUATIONS
A NOTE ON THE BOUNDEDNESS OF SOLUTIONS OF LINEAR PARABOLIC EQUATIONS
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关于线性抛物方程组解有界性的注解
DOI：
10.1090/s0002-9939-1962-0136867-0
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发表时间：
1962
期刊：
影响因子：
--
通讯作者：
A. McNabb
中科院分区：
文献类型：
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作者：
A. McNabb
在具有边界9 B的有界域B中。在本文中，他们的方法略有修改，以证明以下定理。用D表示半无限柱体I（x，t）：xEB，t >}，用D表示其闭包，用DT表示D与半空间t的交点？T.设u = u（x）是方程（1）的解，它在B中连续，是B的闭包，在θ B中为零，在B中有连续的二阶导数.再次，假设w= w（x，t）被定义并且在封闭区域DT中连续，在t = 0时在B上为正，并且对于所有的t 0 0，在9 B上为正，并且具有满足抛物方程的连续导数Ow/Ot，O2 W/OxiOxX
in a bounded domain B with boundary 9B. In this note, their method is slightly modified to prove the following theorem. Denote by D the semi-infinite cylinder I (x, t): xEB, t > } }, by D its closure and by DT the intersection of D with the half-space t ?T. Suppose u = u(x) is a solution of equation (1) which is continuous in B the closure of B, vanishes on 9B and has continuous second derivatives in B. Again, suppose w= w(x, t) is defined and continuous in the closed region DT, is positive on B at t = 0 and on 9B for all t 0 O and has continuous derivatives Ow/Ot, O2W/OxiOxX which satisfy the parabolic equation