The Analysis of Hyers–Ulam Stability for Heat Equations with Time-Dependent Coefficient
The Analysis of Hyers–Ulam Stability for Heat Equations with Time-Dependent Coefficient
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DOI：
10.3390/math10224355
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发表时间：
2022-11
期刊：
影响因子：
2.4
通讯作者：
Fa-bing Wang;Yingcai Gao
中科院分区：
文献类型：
--
作者：
Fa-bing Wang;Yingcai Gao
本文证明了方程ut（x，t）=a（t）Δu（x，t）在初始条件u（x，0）=f（x）下的Hyers-Ulam稳定性和广义Hyers-Ulam稳定性，其中x∈Rn且0<t<T.利用方程基本解的性质证明了上述结果。
In this paper, we prove the Hyers–Ulam stability and generalized Hyers–Ulam stability of ut(x,t)=a(t)Δu(x,t) with an initial condition u(x,0)=f(x) for x∈Rn and 0<t<T; the corresponding conclusions of the standard heat equation can be also derived as corollaries. All of the above results are proved by using the properties of the fundamental solution of the equation.