TY - JOUR
T1 - Higher Order Dissipative-Dispersive System and Application
AU - Israwi , Samer
JO - Journal of Partial Differential Equations
VL - 3
SP - 261
EP - 274
PY - 2020
DA - 2020/06
SN - 33
DO - http://doi.org/10.4208/jpde.v33.n3.6
UR - https://global-sci.org/intro/article_detail/jpde/17074.html
KW - Cauchy problem, Euler system, dispersive wave equation, Camassa-Holm equation.
AB - <p style="text-align: justify;">In this paper, a generalized nonlinear dissipative and dispersive equation
with time and space-dependent coefficients is considered. We show that the control of
the higher order term is possible by using an adequate weight function to define the
energy. The existence and uniqueness of solutions are obtained via a Picard iterative
method. As an application to this general Theorem, we prove the well-posedness of
the Camassa-Holm type equation.</p>