Analytical solution for descriptor system in partial differential equations

We consider a first-order partial differential equation with constant irreversible coefficients in a Banach space in the regular case. The equation is split into equations in subspaces, in which non-degenerate subsystems are obtained. We obtain an analytical solution of each system with Showalter-type conditions. Finally, an example is given to illustrate the theoretical results.

Analytical solution for descriptor system in partial differential equations Keywords:

Banach Space , descriptor system , Differential algebraic equations , 0-normal eigenvalue , Showalter-type conditions