BrainMap

Radu Precup

- UNIVERSITATEA BABES BOLYAI

Expertise & keywords

Operator Methods for Nonlinear Systems and Applications Call name: Exploratory Research Projects - PCE-2011 call
PN-II-ID-PCE-2011-3-0094 2011 - 2016

Role in this project: Project coordinator

Coordinating institution: Universitatea Babes-Bolyai Cluj-Napoca

Project partners: Universitatea Babes-Bolyai Cluj-Napoca (RO)

Affiliation: Universitatea Babes-Bolyai Cluj-Napoca (RO)

Project website: https://sites.google.com/site/pce0094/

Abstract:

The goal of this project is to develop the vector operator method for the study of nonlinear systems. The operator approach is based on the representation of problems under an operator form, as fixed point equations, coincidence or zero type equations. The vector approach allows a more relaxed treatment of systems which may include equations whose nonlinear terms can have different behaviors. The vector approach does not reduce a system to a single equation in Rn and makes use instead of usual scalar norms and metrics, Lipschitz and growth constants, of vector-valued norms and metrics, and of Lipschitz and growth matrices. Vector approach requires the vectorization of the corresponding tools from nonlinear analysis: fixed point principles, degree theory, critical point theory and approximation methods. Our main goal is to develop the method both in theory (fixed point theory and critical point theory), numerical computation and concrete applications. Guiding by the leading concept of vector operator method, a number of specific problems will be in our attention: 1. Localization and multiplicity of positive solutions by means of compression-expansion conditions; 2. The existence and stability of periodic solutions for differential systems; 3. Analysis of a three-dimensional system from mathematical medicine; 4. Compensation of compactness by properties of an order relation; 5. Nonlinear analysis under less regular frameworks; 6. Efficient numerical and computational methods.

DIFFERENTIAL SYSTEMS IN NONLINEAR ANALYSIS AND APPLICATIONS Call name: Complex Exploratory Research Projects - PCCE-2008 call
PN-II-ID-PCCE-2008-0055 2010 - 2013

Role in this project: Partner team leader

Coordinating institution: UNIVERSITATEA DIN CRAIOVA

Project partners: UNIVERSITATEA DIN CRAIOVA (RO); INSTITUTUL DE MATEMATICA SIMION STOILOW AL ACADEMIEI ROMANE (RO); UNIVERSITATEA BABES-BOLYAI DIN CLUJ-NAPOCA (RO)

Affiliation: UNIVERSITATEA BABES-BOLYAI DIN CLUJ-NAPOCA (RO)

Project website: http://www.inf.ucv.ro/~annel

Abstract:

The project has as objectives the study of fundamental mathematical models from the fields of nonlinear and differential analysis systems in order to highlight their results in mathematical physics, in the information theory and bio-mathematical system. The subject addressed by the project, represents the latest milestone in the applied mathematics research field. The research consortium has the purpose of binding together all the knowledge gain by each research group in order to emphasize fundamental models from the equation's theory of non-homogeneous partial derivatives, degenerated and singular equations, nonsupersingular elliptic equations; the potential theory and Markov's ramification processes. In this way, the general objective of the project is a fundamental interdisciplinary study. The scope of the project implies the following basic aspects: a) the creation of mathematical models used in the study of non-homogeneous partial derivatives, degenerated, singular, particular cases of nonsupersingular elliptic equations systems and the analysis of the models created by using the potential theory, and also the extension of these models by ramification process equations. b) the way in which these model are used in the study of information security, extended to the study of the theory of information, with appliance in the theory of codes. The way in which the results are used in the study of bio-mathematical models, with appliances in evolution models of compounds, which in turn are being used to evaluate the time splits in biochemical phenomenons, used in the research of some biological phenomenons. The project integrates the expertise domains of three Romanian research groups: from the University of Craiova, The Mathematical Institute of the Romanian Academy and University Babeş-Bolya of Cluj-Napoca. Due to the equal distribution and different fundamental and applicative research fields, an interdisciplinary collaboration activity will take place. Each group has members with long experience in their domains of activity, facts that are being emphasized by precedent research contracts, by articles and notes published on their filed of expertise and by the effective results obtained in their research's direction.

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List of research grants as project coordinator or partner team leader
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