Institute of Mathematics and Mechanics
Azerbaijan National Academy of Science

Department of “Equations of mathematical physics”


Head of the department: Rauf Veli oglu Guseynov
Doctor of physico-mathematical sciences, professor, corresponding member of NASA
Tel: (+994 12)  5387250
Number of employees: 12
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.
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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