Objective
The project lies in the area of nonlinear analysis, dealing with nonlinear differential equations, mainly of elliptic and parabolic type. The emphasis is on the rigorous qualitative theory, with a strong basis in analysis, classical and functional. It also uses the machinery of ordinary differential equations and some geometrical and topological methods as well as numerical adaptive techniques. In particular, we consider the equations occurring as ground states in the field equations, as models for diffusive, convective and/or reactive processes, as ignition paradigms or flame models in combustion. The published works of the participants show these applied aspects.
There are four main jects of common interest between the 7 teams, namely:
Nonlinear evolution equations (and systems) appearing in the description of
a number of physical processes, mainly the thermal propagation, flows in
porous media, reaction-diffusion processes of different types.
The stationary states which usually take the form of nonlinear elliptic
equations. These equations appear frequently as ground states in field
equations or (rescaled) stationary profiles of selfsimilar processes.
Singularities of different types arising in these nonlinear problems. The
most important are: shocks in gas dynamics equations (called usually in the
mathematical literature nonlinear conservation laws), free boundaries
boundary layers (typical in fluid mechanics), blow-up (one of the main
mathematical aspects of combustion theory), quenching and extinction
phenomena (important in reaction dynamics).
The exploitation of geometrical or group theoretical properties is a great
help in the study of nonlinear problems. The use of self-similarity has been a constant interest of the Russian and English teams involved. The practical interaction will take place through a number of individual visits, plus electronic communications.
Topic(s)
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BA2 7AY BATH
United Kingdom