EDPNOL

The main objective of this research group is to develop new methods for nonlinear partial differential equations that allow us to contribute to the solution of concrete problems, most of them suggested by applications. Nonlinear phenomena in partial differential equations are a central theme in their application to science, engineering and industry, and in the modern theoretical development of the theory of partial differential equations itself. In this group we will focus on the study of some nonlinear partial differential equations that model problems coming from different areas such as: image processing, materials science and crystal growth, phase transition problems whose free energy functional has linear growth with respect to the gradient, nonlinear diffusion problems and hydrodynamic radiation theory. In telegraphic form the topics we are interested in are the following: Degenerate parabolic equations with saturated flow. Models for the dynamics of granular materials. Degenerate hyperbolic-parabolic equations. Diffusion equations with gradient-dependent terms. Non-linear elliptic equations involving measured data. The inhomogeneous Dirichlet problem for the p-Laplacian. Uniqueness for elliptic equations with lower-order terms. Non-local evolution problems. The 1-harmonic flow.