This book contains the major works of Ivan Georgievich Petrowsky on systems of partial differential equations and algebraic geometry. The articles are of crucial importance for the topology of real algebraic manifolds and are the source of intensive development of theory of real algebraic manifolds.

Each of the articles is accompanied by the editor's notes. In addition, each article has been studied (and, in parts, corrected) by modern Russian mathematicians and appears with their commentaries.
This deals with the theory of systems of partial differential equations and is central to the modern general theory of such systems. It was in these works that the classes of elliptic, hyperbolic, and paranbolic systems were singled out and studied for the first time. These articles are at the origin of vast and important disciplines in the theory of partial differential equations and its applications.

In 1993, Professor Oleinik was invited to give a series of lectures about her work in the area of partial differential equations. This book contains those lectures, and more. It is in two parts, the first being devoted to the study of the asymptotic behaviour at infinity of solutions of a class of non-linear second order elliptic equations in unbounded, in particular cylindrical, domains. Questions of this type occur in many areas of mathematical physics, such as in the theory of travelling waves, homogenisation, boundary layer theory, flame propagation and combustion. The second part contains the most recent results of the author's research in the theory of homogenisation of partial differential equations, and is concerned with questions about partially perforated domains and of solutions with rapidly alternating types of boundary conditions. These asymptotic problems arise naturally in applications. Many of the results here have not appeared in book form before, and this volume sheds light on the subject, raising many ideas and open problems.

In 1993, Professor Oleinik was invited to give a series of lectures about her work in the area of partial differential equations. This book contains those lectures, and more. It is in two parts, the first being devoted to the study of the asymptotic behaviour at infinity of solutions of a class of non-linear second order elliptic equations in unbounded, in particular cylindrical, domains. Questions of this type occur in many areas of mathematical physics, such as in the theory of travelling waves, homogenisation, boundary layer theory, flame propagation and combustion. The second part contains the most recent results of the author's research in the theory of homogenisation of partial differential equations, and is concerned with questions about partially perforated domains and of solutions with rapidly alternating types of boundary conditions. These asymptotic problems arise naturally in applications. Many of the results here have not appeared in book form before, and this volume sheds light on the subject, raising many ideas and open problems.