Browsing by Author "Shakhmurov,V.B."

Now showing 1 - 5 of 5

Citation Count: 2
The Cauchy problem for generalized abstract Boussinesq equations
(Dynamic Publishers, 2016) Shakhmurov,V.B.
In this paper, the existence and uniqueness of solution of the Cauchy problem for abstract Boussinesq equations is obtained. By applying this result, the Wentzell-Robin type mixed problem for Boussinesq equations and the Cauchy problem for finite or infinite systems of Boussinesq equations are studied. © Dynamic Publishers, Inc.
Citation Count: 0
Degenerate abstract parabolic equations and applications
(Mathematical Research Publishers, 2015) Shakhmurov,V.B.; Sahmurova,A.
Linear and nonlinear degenerate abstract parabolic equations with variable coefficients are studied. Here the equations and boundary conditions are degenerated on all boundary and contain some parameters. The linear problem is considered on the moving domain. The separability properties of elliptic and parabolic problems and Strichartz type estimates in mixed Lp spaces are obtained. Moreover, the existence and uniqueness of optimal regular solution of mixed problem for nonlinear parabolic equation is established. Note that, these problems arise in fluid mechanics and environmental engineering.
Citation Count: 2
Mixed problems for degenerate abstract parabolic equations and applications
(SINUS Association, 2018) Shakhmurov,V.B.; Sahmurova,A.
Degenerate abstract parabolic equations with variable coefficients are studied. Here the boundary conditions are nonlocal. The maximal regularity properties of solutions for elliptic and parabolic problems and Strichartz type estimates in mixed Lebesgue spaces are obtained. Moreover, the existence and uniqueness of optimal regular solution of mixed problem for nonlinear parabolic equation is established. Note that, these problems arise in fluid mechanics and environmental engineering. © 2018, SINUS Association. All rights reserved.
Citation Count: 5
Separable differential operators and applications
(Independent University of Moscow, 2016) Shakhmurov,V.B.
The nonlocal boundary value problems for degenerate differential-operator equations with variable coefficients are studied. The Lp separability properties of elliptic problems and well-posedeness of parabolic problems in mixed Lp spaces are derived. Then by using the regularity properties of linear problems, the existence and uniqueness of solution of nonlinear elliptic problem is obtained. Note that applications of these problems can be models of different physics process. © 2016 Independent University of Moscow.
Citation Count: 0
Singular degenerate problems occurring in atmospheric dispersion of pollutants
(Springer International Publishing, 2014) Sahmurova,A.; Shakhmurov,V.B.
The boundary value problems for singular degenerate linear and regular degenerate nonlinear differential-operator equations are studied. We prove the well-posedeness of the linear problem and optimal regularity result for the nonlinear problem which occur in fluid mechanics, environmental engineering and in the atmospheric dispersion of pollutants. © 2014 Springer Basel.