Abstract
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.
Funder
Hunan Provincial Education Department Project
National Natural Science Foundation of China
Graduate Research Innovation Project of Changsha University of Science and Technology
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)