| Head of the department: |
Rauf Veli oglu Guseynov
Doctor of physico-mathematical sciences, professor, corresponding member of NASA |
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| Tel: |
(+994 12) 5387250 |
| E-mail: |
[email protected], r[email protected] |
| Number of employees: |
12 |
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| The basic scientific direction of the department: |
- On-valued solvability of different boundary value problems for divergent and non-divergent structure linear and nonlinear quasi-elliptic equations and non-stationary equations with quasi-elliptic part;
- investigation of quality properties of solutions of nonlinear pseudo-hyperbolic equations;
- studying of direct and inverse problems.
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| The obtained basic scientific results: |
- Negative spectra of quasi-elliptic equations were studied, their number was estimated;
- the results expressing quality properties of divergent and non-divergent structure second order degenerate and non-degenerate elliptic and parabolic equations were obtained;
- equivalence of Wiener and Petrovsky type criteria of regularity of the point of a boundary value problem for parabolic equations was proved;
- quality properties of solutions of non-divergent structure, discontinuous coefficient parabolic equations were studied;
- ”conditional” well-posedness of inverse problems with coefficient for linear, nonlinear, quasi-linear parabolic equations and system of equations was studied;
- quality properties of the solutions of a class of pseudo-hyperbolic and pseudo-parabolic equations were investigated;
- parabolic potentials were estimated in singular domains;
- asymptotics of the solutions of nonlinear equations near the singular point was studied;
- Poincare inequality for second order quasi-linear elliptic equations was proved;
- the questions of existence and uniqueness of solutions of the Dirichlet and Neumann problem for discontinuous coefficient Cordes type linear and quasi-linear elliptic equations were studied;
- theorems on a removable singularity of Carleson type for degenerate equations were proved;
- theorems on a removable singularity and theorems on the qualitative properties for p-Laplacian type quasi-linear equations with degenerating principal part were proved;
- Poincare-Sobolev and Hardy type uniform and non-uniform inequalities were proved;
- weighted Hardy inequalities in the Lebesgue spaces with a variable exponent were proved;
- existence of global solutions of semi-linear elliptic and parabolic type equations were studied, exact estimations for the existence of solutions were found;
- asymptotics of solutions satisfying the Neumann condition near the infinity was studied;
- uniqueness of solution of linear ordinary differential and partial equations without boundary condition was studied;
- behavior of Zaremba problem for second order degenerate elliptic equations in the boundary was studied, regularity of congruence point in special spherical layers was investigated.
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