University of Tabriz Computational Methods for Differential Equations 2345-3982 9 2 2021 04 01 Analytical solution for descriptor system in partial differential equations 467 479 12686 10.22034/cmde.2021.42195.1824 EN Svetlana Petrovna Zubova Department of mathematical Analysis, Faculty of Mathematics,\\Voronezh State University, Voronezh, Russia. Abdulftah Hosni Mohamad Department of mathematical Analysis, Faculty of Mathematics,\\Voronezh State University, Voronezh, Russia. Journal Article 2020 10 09 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<br /> results. Banach Space descriptor system Differential algebraic equations 0-normal eigenvalue Showalter-type conditions https://cmde.tabrizu.ac.ir/article_12686_425b7d32c369dafd54ba4f58a734c16b.pdf