Nonlinear Partial Differential Equations - EDPNOL

Reference of the Group:

GIUV2013-040

 
Description of research activity:
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...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.
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Web:

http://edenol.blogs.uv.es

 
Scientific-technical goals:
  • Regularidad de las soluciones de la ecuacion relativista del calor
  • Problemas de reaccion-difusion (Fisher-Kolmogorov, Patlak-Keller-Segel, ect.) con la difusion relativa a la ecuacion relativista del
  • Existencia de soluciones para ecuaciones de difusion con terminos dependientes del gradiente
  • Problemas de transporte de masas
  • Existencia y unicidad para el flujo 1-armonico
 
Research lines:
  • Partial differential equations.To develop new methods for non-linear partial differential equations that allow us to contribute to solving specific problems, most of them brought about by applications.
 
Group members:
Name Nature of participation Entity Description
JOSE M MAZON RUIZDirectorUniversitat de València
Research team
SERGIO SEGURA DE LEONMemberUniversitat de València
JOSE JULIAN TOLEDO MELEROMemberUniversitat de València
JOSE SALVADOR MOLL CEBOLLAMemberUniversitat de València
MARCOS SOLERA DIANAMemberUniversitat de València
 
CNAE:
  • -
 
Associated structure:
  • Mathematical Analysis
 
Keywords:
  • ecuaciones parabólicas; ecuaciones elípticas;teoría del transporte; cálculo de variaciones