Nonlinear Dunkl-wave equations

Abstract

In this article, we introduce a class of nonlinear wave equations associated with the Dunkl operators, we study local and global well-posedness. Next, we establish the linearization of bounded energy solutions in the spirit of Gérard [P. Gérard, Oscillations and concentration effects in semilinear dispersive wave equations, J. Funct. Anal. 141 (1996), pp. 60–98]. The proof uses Strichartz-type inequalities and the energy estimate.

Keywords:

• Dunkl operators
• Dunkl-wave equation
• Strichartz estimates

AMS Subject Classification:

• 35Q55