The fundamental objective of this research group is to develop new methods for nonlinear partial differential equations that will allow us to contribute to the solution of specific problems, most of them suggested by applications. Nonlinear phenomena in partial differential equations are a central topic due to 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 from different areas such as image processing, materials science and crystal growth, phase transition problems whose free energy functionals have linear growth with respect to the gradient, nonlinear diffusion problems, and hydrodynamic radiation theory. In brief, the topics we are interested in are the following:
1. Degenerate parabolic equations with saturated flow.
2. Models for the dynamics of granular materials.
3. Degenerate hyperbolic-parabolic equations.
4. Diffusion equations with gradient-dependent terms.
5. Nonlinear elliptic equations with measured data.
6. The nonhomogeneous Dirichlet problem for the p-Laplacian.
7. Uniqueness of elliptic equations with lower-order terms.
8. Nonlocal evolution problems.
9. 1st-harmonic flow.
