Special Session #14

Partial differential equations with nonstandard growth and applications
Hermenegildo Borges de Oliveira1, Sergey Shmarev2


In recent years, Partial Differential Equations with nonstandard growth conditions have become a major area of research. These equations, which include PDEs with variable nonlinearity and anisotropic equations, pose significant mathematical challenges. At the same time, mathematical models based on PDEs with  nonstandard growth offer more precise modeling of many real-life processes, such as flows of non-Newtonian fluids or processing of digital images. The study of these equations requires the development of specific tools such as the theory of variable Lebesgue and Sobolev spaces or Musielak-Orlicz spaces. The aim of the session is to gather specialists in these topics for an exchange of the state-of-art results.

List of topics of interest:

• existence and uniqueness results,

• qualitative properties and regularity of solutions,

• asymptotic behavior,

• mathematical models based on PDEs with nonstandard growth,

• numerical simulation,

• analytical tools for the study of PDEs with nonstandard growth.