Danh Hua Quoc Nam.

Homogeneous Parabolic Equation on the Sphere  with Nonlocal Initial and Final Conditions. Dynamic Systems and Applications 30 (2021) No.1, 131-142

https://doi.org/10.46719/dsa20213019

ABSTRACT.  
The paper is devoted to   the  regularity result of solutions  for parabolic equation on the sphere  with nonlocal initial and final conditions.   Using some techniques of the Fourier series and Parseval’s equality,  we show the well-posedness result of our problem.  Finally, we prove that the solution of our problem converges to the solution of the initial value problem and the final value problem when the two parameters a, b approach zero. This paper extends to the recent paper: Solving the backward heat equation on the unit sphere , ANZIAM J. (E) 56 (2016), pp. C262–C278.

 AMS (MOS) Subject Classification. 35K05, 35K99, 47J06, 47H10.

Keywords and phrases:  Parabolic equation;  Sphere; Nonlocal conditions; Well-posedness and regularity.