Hoang Tuan Nguyen, Nguyen Anh Triet, and Ho Thi Kim Van. Approximation of a Sideways Problem for Nonlinear Space Fractional Heat Equation. Dynamic Systems and Applications 30 (2021) No.3, 331-346

https://doi.org/10.46719/dsa20213032

ABSTRACT.
Our main goal in this paper is to considering a sideways problem for parabolic equation with Caputo derivative.  Fractional models appear in this paper  has many applications for  modeling various memory phenomena.  We show that  the problem is ill-posed in the sense of Hadamard in both cases: linear and nonlinear source terms. We also give the positive answer for   the open-ended question that of   B. Jin and W. Rundell in their paper {\it “A tutorial on inverse problems for anomalous diffusion processes, Inverse Problems”. By applying  Fourier truncation regularization method, we set up a regularized solution.  Under an a priori hypothesis of the sought solution,  we obtain the convergence error estimates between the regular solution and the exact solution.

Keywords:  Caputo fractional derivative, ill-posedness,  regularity estimates; sideways heat equation   

 AMS (MOS) Subject Classification. 39A10.