Special Session 31

Recent Trends in Nonlinear Elliptic and Parabolic PDEs

Organizers: Cristina Tarsi (University of Milan, Italy), Joao Marcos do O (Federal University of Paraíba, Brazil)

MSC codes: 35J15, 35K10

Description:

Nonlinear elliptic and parabolic partial differential equations govern a wide range of complex phenomena, including population dynamics, combustion theory and fluid dynamics. Understanding their qualitative properties is essential for gaining deeper insight into these multifaceted processes. This session focuses on fundamental issues such as existence, non-existence, uniqueness and multiplicity of solutions, asymptotic behaviour, blow-up, singularity formation and bubbling phenomena. Particular emphasis is placed on geometric and functional inequalities as key analytical tools for advancing the study of nonlinear equations. The aim of this special session is to bring together researchers working in these areas, fostering focused discussion and exchange of ideas that may stimulate further developments and identify open problems.