BrainMap

Mrs. Maria Farcaseanu

Ph.D.

Researcher - INSTITUTUL DE STATISTICA MATEMATICA SI MATEMATICA APLICATA AL ACADEMIEI ROMANE''GHEORGHE MIHOC - CAIUS IACOB'

Researcher

Web of Science ResearcherID: AAV-2700-2020

Curriculum Vitae (28/10/2022)

Expertise & keywords

Exploring properties of several classes of partial differential equations Call name: P 1 - SP 1.1 - Proiecte de cercetare Postdoctorală - PD-2021
PN-III-P1-1.1-PD-2021-0037 2022 - 2024

Role in this project:

Coordinating institution: INSTITUTUL DE STATISTICA MATEMATICA SI MATEMATICA APLICATA AL ACADEMIEI ROMANE''GHEORGHE MIHOC - CAIUS IACOB'

Project partners: INSTITUTUL DE STATISTICA MATEMATICA SI MATEMATICA APLICATA AL ACADEMIEI ROMANE''GHEORGHE MIHOC - CAIUS IACOB' (RO)

Affiliation:

Project website: https://sites.google.com/site/mariafarcaseanu/research-projects/pd-2021-0037

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.

The Infinity-Laplace Operator Call name: P 1 - SP 1.1 - Proiecte de cercetare pentru stimularea tinerelor echipe independente
PN-III-P1-1.1-TE-2019-0456 2020 - 2022

Role in this project:

Coordinating institution: UNIVERSITATEA POLITEHNICA DIN BUCURESTI

Project partners: UNIVERSITATEA POLITEHNICA DIN BUCURESTI (RO)

Affiliation: UNIVERSITATEA POLITEHNICA DIN BUCURESTI (RO)

Project website: https://sites.google.com/site/denisastancudumitru/grant-te

Abstract:

In this project we are concerned with the study of some classes of Partial Differential Equations (PDE’s) involving the presence of the Infinity-Laplace operator. There are several research directions undergirding the topic of the present project: the Absolutely Minimizing Lipschitz Extension Problem (AMLE Problem) of Aronsson, the Torsional Creep Problem – studied by Kawohl and Bhattacharya-DiBenedetto-Manfredi, and The ∞-Eigenvalue Problem – investigated by Juutinen-Lindqvist-Manfredi. The motivation to study PDE’s involving the Infinity-Laplace operator partially stems from its usefulness in certain applications such as optimal transportation, image processing or tug-of-war games. Motivated by the classical problems recalled above, we propose the analysis of at least three related problems which represent the main objectives of our proposal and are expected to complete the existing knowledge to date on the topic: the study of the AMLE problem for non-uniformly elliptic operators (including the cases of Grushin-type operators and double phase type operators); the analysis of some torsional creep problems in Finsler metrics; the investigation of the asymptotic behavior of some new families of eigenvalue problems. We expect that the papers that will be published at the end of this grant will be of interest for researchers working not only in the domain of mathematics but in mathematical physics, fluid dynamics or game theory.

Typical and Nontypical Eigenvalue Problems for Some Classes of Differential Operators Call name: P 4 - Proiecte de Cercetare Exploratorie
PN-III-P4-ID-PCE-2016-0035 2017 - 2019

Role in this project: Key expert

Coordinating institution: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE

Project partners: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Affiliation: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Project website: https://sites.google.com/site/mmihailes/grant-cncs-uefiscdi-pn-iii-p4-id-pce-2016-0035

Abstract:

In literature a "typical eigenvalue problem" is commonly related with a linear differential equation. A basic example in the elementary theory of linear Partial Differential Equations (PDEs) concerns the eigenvalue problem for the Laplace operator on a bounded domain from the Euclidian space, subject to the homogeneous Dirichlet boundary condition. For this problem one can describe its entire spectrum as being a nondecreasing and unbounded sequence of positive real numbers. In the case of the nonlinear eigenvalue problems involving the p-Laplacian with p a given constant in (1,∞) and p≠2 the homogeneity of the problem enables us to consider that it still possesses the structure of a "typical eigenvalue problem". However, the nonlinear character of the problem induces some complications in describing the set of all eigenvalues of the problem. It is known that the Ljusternik-Schnirelman theory ensures the existence of a nondecreasing and unbounded sequence of positive eigenvalues but in general this theory does not provide all eigenvalues. There are many other open questions concerning the set of eigenvalues of the nonlinear p-Laplacian. Next, we recall that even much less in known for the case of "nontypical eigenvalue problems" when the structure of the problem involves inhomogeneous differential operators. Finally, we point out that eigenvalue problems could also be regarded as a starting point in analyzing more complicated equations. Thus, alongside the study of the classical open questions from the topic (where we are aware of the fact that solving such kind of problems could be extremely difficult), in this project we propose the analysis of the following directions of research: the classification of isolated singularities for some PDEs; the analysis of a Rayleigh-type quotient corresponding to some eigenvalue problems involving rapidly growing differential operators; the study of some inhomogeneous torsional creep problems.

Analysis of Schrödinger equations Call name: Projects for Young Research Teams - RUTE -2014 call
PN-II-RU-TE-2014-4-0007 2015 - 2017

Role in this project: Key expert

Coordinating institution: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE

Project partners: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Affiliation: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Project website: https://sites.google.com/site/liviuignat/projects/grant-te2015-2017

Abstract:

In this project we consider deterministic and stochastic Schrödinger equations on metric graphs. By using fine tools from harmonic analysis and stochastic analysis we study the dispersion property in terms of the topology of the considered structure. We analyze the well-posedness of nonlinear models and study some of their qualitative properties: long time behavior, solitons, waves propagation, blow-up, scattering. We investigate the influence of the graph topology on the behavior of the solutions, the existence of maximizers for Strichartz –like estimates and the way they depend on the topology. Discrete models of the above equations will be considered both from the numerical as the theoretical point of view.

Variable Exponent Analysis: Partial Differential Equations and Calculus of Variations Call name: Exploratory Research Projects - PCE-2012 call
PN-II-ID-PCE-2012-4-0021 2013 - 2016

Role in this project: Key expert

Coordinating institution: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE

Project partners: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Affiliation: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Project website: https://sites.google.com/site/mmihailes/grant-cncs-uefiscdi-pn-ii-id-pce-2012-4-0021

Abstract:

Variable exponent analysis has its roots in the study of functional spaces involving variable exponents primarily due to Orlicz’s works from the 1930’s. The topic has benefited from constant interest over the years, and in the last decades substantial scholarly attention has been increasingly given to this research area in connection with the study of some PDE’s which can serve as models for different phenomena arising in elasticity theory, fluid dynamics, image processing or mathematical biology. The differential operator usually involved in such equations is the p(x)-Laplace operator and it represents an adequate candidate for modeling nonhomogeneous processes which can occur in different real world applications. At the same time, the competition of growth rates involved in equations with variable exponents enables more situations of study than in the case when constant coefficients are involved. The papers where such kinds of problems are treated usually do not cover all the situations that can occur, generally being just isolated results which are mostly applied on some special cases. There are many open challenging problems and unanswered mathematical questions in this field making the study of equations with variable exponents extremely attractive.

FILE DESCRIPTION	DOCUMENT
List of research grants as project coordinator or partner team leader
Significant R&D projects for enterprises, as project manager
R&D activities in enterprises
Peer-review activity for international programs/projects