Abstract:
Partial differential equations of the third order are the basis of mathematical models of many phenomena
and processes, such as the phenomenon of energy transfer of hydrolysis of adenosine triphosphate molecules
along protein molecules in the form of solitary waves, i.e. solitons, the process of transferring soil moisture in
the aeration zone, taking into account its movement against the moisture potential. In particular, this class
includes the nonlinear Korteweg-de Vries equation, which is the main equation of modern mathematical
physics. It is known that various problems have been studied for the Korteweg-de Vries equation and many
fundamental results obtained. In this paper, issues about the existence of a resolvent and separability
(maximum smoothness of solutions) of a class of linear singular operators of the Korteweg-de Vries type in
the case of an unbounded domain with strongly increasing coefficients are investigated.
