Regularization of a Cauchy problem for the heat equation
Regularization of a Cauchy problem for the heat equation
In this paper, we study a Cauchy problem for the heat equation with linear source in the form ut(x,t)= uxx(x,t)+f(x,t), u(L,t)= φ(t), u(L,t)= Ψ (t), (x,t) ∈ (0,L) ×(0, 2π). This problem is ill-posed in the sense of Hadamard. To regularize the problem, the truncation method is proposed to solve …