Nonlinear Elliptic and Parabolic Problems
This book is the proceedings of a conference held in Zürich, Swirtzerland, in 2004. It contains about thirty articles, mostly dealing with areas where H. Amann made an important contribution. It could be said that the mathematical problem behind all the articles is the nonlinear elliptic/parabolic equation ∂t u - ∆u + f(x,u, grad u) = 0 or a system of such equations. The articles could be roughly divided into three groups. (i) Papers dealing with a single equation of the above type in its simplest form. In such a case, quite a detailed description of the qualitative behaviour can usually be given. (ii) Systems of equations of the above type that have a clear physical, technical or biological application (the incompressible, homogeneous Navier-Stokes equations are a particular example). (iii) Abstract functional analytic problems, bifurcations, and the properties of function spaces arising in connection to an equation of the above type. The papers usually contain new results but many of them also provide a longer survey of results for the particular area.