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SINGULAR AND DEGENERATE EVOLUTION PROBLEMS |
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SINGULAR AND DEGENERATE EVOLUTION PROBLEMS |
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The theory of non-linear partial differential equations (PDEs) is of fundamental importance in mathematical analysis and through recent breakthroughs it has become an even more active field. In the meeting we want to address a large and important class of non-linear partial differential equations and systems, namely singular and degenerate non-linear parabolic PDEs. In this case, there are several phenomena and difficulties which are not present in the corresponding, time-independent elliptic case. For example, disturbances may have a finite speed of propagation or there may be an extinction phenomenon in finite time. These are often natural properties in applications. Although singular and degenerate PDEs have a common structure, they are connected to many different applications such as the diffusion in highly nonhomogeneous and anisotropic media, the motion of multi-phase fluids and flow through porous media. The velocity gradient of these fluids depends in a non-linear way on the stress tensor and this kind of phenomena occur, for instance, in glaceology, rheology, mean curvature flow and non-linear elasticity. Other applications include behaviour of composite materials, image processing, stochastic game theory, and pricing the assets in financial markets. A crucial role in understanding non-linear phenomena is played by regularity estimates that are based only on the structure of the equations under consideration. Indeed, solutions of non-linear partial differential equations, when they exist, are not a priori smooth. During the last few decades a vast amount of research papers have been published and powerful techniques have been developed to understand the behaviour of weak solutions. In several ways, recent breakthroughs open up a whole new area of research similar to the progress that started a few decades ago concerning regularity and free boundary regularity for linear PDEs, and these new results have already proved powerful enough to solve previously unreachable problems in regularity theory. The meeting is part of an on-going collaboration among scholars from many different countries. The invitees form a cohesive group of researchers who have shared ideas for a long time and some of them have joint contributions. The aim is to bring together the leading experts in the field, postdoctoral researches and graduate students, in order to discuss and share ideas on the major open problems, to suggest novel research perspectives, and to develop new scientific connections. Junior people are encouraged to strongly interact with the senior researchers, and to work in current research projects in collaboration with them. In particular, this meeting would like to strengthen the international contacts, and further develop the existing activities. |
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J. Kinnunen (Aalto University): Nonlinear parabolic capacity theory
H.-D. Alber (Darmstadt)
The program of the workshop consists of two 4h minicourses, and 30' or 40' invited lectures.
INdAM - Istituto Nazionale di Alta Matematica
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Palazzone (Villa Passerini)
No fee is required, but a registration is needed. This can be done here
How to get to Cortona
Registration deadline: May 15th 2014
Please feel free to contact the Workshop office desk by: |
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Workshop aims