Application of Tikhonov's regularization to unstable water waves of the two-dimensional fluid flow: spectrum with compact support

Abstract

The primary objective of this paper is to examine the instability of the two-dimensional initial value problem for dispersive water waves for a certain class of initial conditions. It is found that the phenomenon of instability is closely related to a compact operator as well as a spectrum function with a compact support. Tikhonov's regularization method is introduced to treat the instability of obtaining a stable solution. Numerical experiments are carried out to find that numerical solutions by the regularization procedure turn out to be stable and accurate.

Key words:

• Phenomenon of instability
• compact operator
• compact support
• Tikhonov's regularization method

ACKNOWLEDGMENT

This work was supported for two years by Pusan National Research Grant.