Volume 16, Number 1, Spring 2008
NONLINEAR DISPERSIVE WAVES ON TREES
JERRY L. BONA AND RADU C. CASCAVAL
Abstract. We investigate the well-posedness of a class
of nonlinear dispersive waves on trees, in connection with the
mathematical modeling of the human cardiovascular system.
Specifically, we study the Benjamin-Bona-Mahony (BBM) equation,
also known as the regularized long wave equation, posed
on finite trees, together with standard junction and terminal
boundary conditions. We prove that the Cauchy problem for
the BBM equation is well-posed in an appropriate space on
arbitrary finite trees.