PN-III-P1-1.1-PD-2021-0037
"Exploring properties of several classes of Partial Differential Equations"
Project Code: PN-III-P1-1.1-PD-2021-0037
Contract no: PD 96/2022
Funding: Ministry of Research, Innovation and Digitization, CNCS - UEFISCDI, within PNCDI III
Period: June 01, 2022 - May 31, 2024
Host Institution: "Gheorghe Mihoc-Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Bucharest
Team: Maria Farcaseanu (project leader), Mihai Mihailescu (mentor)
Abstract: In Mathematics and the Sciences, partial differential equations (PDEs) are a many-faceted subject. Due to the variety of sources, there is a wide spectrum of different types of PDEs and there is no general theory concerning the solvability of all of them. This project aims to provide original approaches and techniques in the analysis of two themes within PDEs field: (a) boundary value problems and (b) the isolated singularity problem. Using as starting point several studies on PDEs involving (p,q)-Laplace type operators, the first objective of the project will focus on the investigation of the existence and asymptotic behavior of positive solutions for a boundary value problem involving more general inhomogeneous differential operators considered in an Orlicz-Sobolev setting. Motivated by the recent advances in the study of the isolated singularity problem for elliptic equations involving singular potentials, the second objective of the project will extend, to the case of systems of the same type, results regarding the existence and profiles near zero of their positive solutions. At the conclusion of the project the results will not only fill a gap in current knowledge in these fields, but will also have cross-disciplinary significance in areas such as mathematical physics, quantum mechanics, fluid dynamics or mathematical biology.
2022
Talks:
15th French-Romanian Colloquium on Applied Mathematics, August 28 - September 3, 2022, Universite Paul Sabatier, Toulouse, France (title of the talk: Classification of singular solutions to nonlinear elliptic equations with a gradient term)
Hausdorff School on Geometric Analysis and Nonlinear Partial Differential Equations, August 8-12, 2022, Hausdorff Center for Mathematics, Bonn, Germany (title of the poster: Isolated singularities for nonlinear elliptic equations with Hardy potential)
International Conference on Applied Mathematics and Numerical Methods, June 29 - 2 July, 2022, University of Craiova, Romania (title of the talk: Classification of singular solutions to nonlinear elliptic equations with a gradient term)
2023
Papers:
M. Farcaseanu, Isolated singularities for semilinear elliptic systems with Hardy potential, J. Math. Anal. Appl. 527 (2023) 127415 .
Talks:
Workshop for Young Researchers in Mathematics - 12th Edition, May 18-19, 2023, Alexandru Ioan Cuza University, Iasi, Romania (title of the talk: Solutions for nonlinear elliptic equations with singular potentials )
Fifth Romanian Itinerant Seminar on Mathematical Analysis and its Applications , May 26-28, 2023, University of Craiova, Craiova, Romania (title of the talk: Radial solutions for nonlinear elliptic equations with singular potentials)
The Tenth Congress of Romanian Mathematicians, June 30 - July 5, 2023, University of Pitesti, Pitesti, Romania (title of the talk: Solutions for nonlinear elliptic equations with singular potentials)
9th International Conference on Mathematics and Informatics, September 8-9, 2023, Sapientia Hungarian University of Transylvania, Targu Mures, Romania (title of the talk: Solutions for nonlinear elliptic equations with singular potentials)
Seminar ISMMA, November 23, 2023, "Gheorghe Mihoc-Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Bucharest, Romania (title of the talk: Isolated singularities for nonlinear elliptic equations with Hardy potential)
2024
Papers:
M. Farcaseanu, M. Mihailescu, D. Stancu-Dumitru: Minimization problem related to the principal frequency of the p-Bilaplacian with coupled Dirichlet-Neumann boundary conditions, Electronic Journal of Qualitative Theory of Diferential Equations 51 (2023)
M. Farcaseanu: Minimizers of rapidly growing operators, preprint.
F. Cirstea, M. Farcaseanu: Nonlinear elliptic equations with singular potentials and gradient-dependent nonlinearities, preprint.
Talks
UAE Math Day 2024, March 2, 2024, New York University Abu Dhabi, Abu Dhabi, Emiratele Arabe Unite, (title of the talk: On the asymptotic behavior of some classes of inhomogeneous equations)