Alexandria Engineering Journal (Dec 2020)

On a final value problem for a nonhomogeneous fractional pseudo-parabolic equation

  • Nguyen Hoang Luc,
  • Devendra Kumar,
  • Le Thi Diem Hang,
  • Nguyen Huu Can

Journal volume & issue
Vol. 59, no. 6
pp. 4353 – 4364

Abstract

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In this paper, we are interested in finding the function u(t,x),(t,x)∈[0,T)×Ω from the final data u(T,x)=ϕ(x), satisfies a nonhomogeneous fractional pseudo-parabolic equation. The problem is stable for the cases σν, the problem is ill-posed (in the sense of Hadamard). We propose the general filtering method to regularize this problem. The well-posedness of the regularized problem and some regularity estimates of the regularized solution are obtained. Moreover, error estimates are established under some a priori conditions of the sought solution. The numerical illustrations are given to show the convergence of our method.

Keywords