Nguyen Duc Phuong and Nguyen Hoang Luc. Note on a Nonlocal Pseudo-Parabolic Equation on the Unit Sphere. Dynamic Systems and Applications 30 (2021) No.2, 295-304

https://doi.org/10.46719/dsa20213029

ABSTRACT.  
Pseudo-parabolic equation on spheres have many important applications in physical phenomena, oceanography and meteorology, geophysics. The main purpose of this paper is to prove the existence and unique solution of the nonlinear  pseudo-parabolic equation on the sphere. To do this, we cleverly employ Banach’s fixed  point theorem, incorporating several evaluations of the spherical harmonics function.  This result is one of the first studies of pseudo-parabolic equations on the sphere.

AMS (MOS) Subject Classification. 35K05, 35K99, 47J06, 47H10x.

Keywords and phrases:  pseudo-parabolic equation;  sphere; nonlocal conditions; well-posedness.