AZƏRBAYCAN MİLLİ ELMLƏR AKADEMİYASI XƏBƏRLƏRİ E LM və İNNOVASİYA seriyasının

1. AZƏRBAYCAN MİLLİ ELMLƏR AKADEMİYASIXƏBƏRLƏRİELM və İNNOVASİYA seriyasının İNNOVASİYA BÜLLETENİ № 8 UOT535.24 DALĞALAR NƏZƏRİYYƏSİNDƏ FORMALARIN OPTİMALLAŞDIRILMASI PROBLEMLƏRİN TƏDQİQATI

2. PROJECT IDEA Project name: Investigation of some shape optimization problems for the different operators with applications to correction of the wave number of the waveguide due optimal corrugated walls and optimization of the cross-sectional shape of the waveguide Proposaloutline: Investigation of the variable domain eigenvalue problems, behavior of the eigenvalues when the domain varies and finding the optimal domains (spectral shape optimization) for the eigenvalues of the Schrödinger operators and for some nonlinear partial differential operator in particular for Laplasian. Developing numerical methods and algorithms for solution of the problems Application of the obtained results for correction of the wave number of the waveguide due optimal corrugated walls and optimization of the cross-sectional shape of the waveguide. Project objectives:(outcomes, socio-economical impacts) It should be noted a wide applications of the considered. For instance, eigenvalues of the Laplace operator indeed are eigenfrequency of the plate under across vibrations. Eigenvalues of the biharmonic operator describe eigenfrequency of the membrane. So, investigation of the dependence of these characteristics on the domain of the plate or membrane, finding of the optimal form for them and other similar problems, as well as, investigation of the properties of the eigenvalues with respect to domain (domain of the plate, for example), related extremal problems (shape optimization problems), developing numerical methods and algorithms for their solution are important not only from theoretical but also from practical points of view . Vilnius, 6-8 November, 2013

3. WANTED Competences & Skills wanted(Technical, Design, Coordination, Writing, etc) Cooperation in discussion of the theoretical results, joint numerical experiments, writing papers, international coordination, participation in international research projects. Types of partners sought(Industry, SME, RTD center, University, User-groups, etc) Universities, Research groups, RTD center Work to be performed(Prototyping, Programming, System Integration, Dissemination, Engineering, etc) Fundamental theoretical results, algorithms, programming, applications

4. SKILLS OF THE PROPOSER Y.S Gasimov – doctor of Sciences, Head of the department of “Inverse problems and non Linear Equations”, supervises some post gradient students, is a specialist on the shape optimization, spectral theory, equation of mathematical physics. He was a visiting professor at the University de Nantes, Nantes, France for joint investigations on the connected topics. He has published a number of papers in international journals with high reputation. He won and held many international projects and grants. M.M. Mutallimov - doctor of Sciences, Head of the department of “Information Computational Systems”, is a specialist on numerical methods, optimization, computer sciences. His papers have been published in various international journals. He participated in many international projects and grants.

5. CONTACTS Name: Gasimov Yusif Mutallimov Mutallim Institution/Organisation: Institute of Applied Mathematis, Baku State University ZIP & City: AZ1148, Baku Country: Azerbaijan Phone number: direct with international code: +(994) 50 3563974 Email: yusif.gasimov@bsu.az , gasimov.yusif@gmail.com mmutallimov@bsu.az Web: http://iam.bsu.edu.az/en/content/gasimov_ys_153 http://iam.bsu.edu.az/en/content/mutallimov_mm_148