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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 new asymptotic problems arise naturally in applications. Many of the results here have not appeared in book form before, and this volume sheds new light on the subject, raising many new ideas and open problems.
Table of contents:
1. Asymptotic problems for non-linear elliptic equations; 2. On the asymptotic behaviour of solutions of some non-linear elliptic equations in cylindrical domains; 3. On the asymptotic behaviour of solutions of some non-linear elliptic equations in a neighbourhood of a conic point of the boundary; 4. On some homogenization 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.
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.
Table of contents:
1. Asymptotic problems for non-linear elliptic equations; 2. On the asymptotic behaviour of solutions of some non-linear elliptic equations in cylindrical domains; 3. On the asymptotic behaviour of solutions of some non-linear elliptic equations in a neighbourhood of a conic point of the boundary; 4. On some homogenization 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.
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.