# (supported by EPSRC Global Challenges Research Fund Knowledge Exchange Scheme)

## Schedule of ODA week (23-28 November 2016)

Wednesday, 23 November, 3—5:30, Imperial College London

Room Clore Lecture Theatre

• 15:00-15:40 Stevan Pilipovic (University of Novi Sad, Serbia) Holder and Besov type regularities in Colombeau algebras of generalized functions

·         Coffee break

• 16:30-17:10 Fikret Aliev (Institute of Applied Mathematics, Azerbaijan) Asymptotical methods for solutions of some identification problems
• 17:20-18:00 Tsegaye Gedif Ayele (Addis Ababa University, Ethiopia) Analysis of two-operator boundary-domain integral equations for variable-coefficient mixed BVP

Thursday, 24 November, 3—5:30, Imperial College London

Room 342

• 15:00-15:40 Mariano Rodriguez (University of Havana, Cuba) “Strong" Turing-Hopf instability for reaction-diffusion systems

·         Coffee break

• 16:30-17:10 Erkinjon Karimov (National University of Uzbekistan, Uzbekistan) Inverse-source non-local problem for mixed type equation with Caputo fractional differential operator
• 17:10-17:50 Fikret Aliev (Institute of Applied Mathematics, Azerbaijan) A method to determine the coefficient of hydraulic resistance in different areas of pump-compressor pipes

Friday, 25 November, 1—4:30pm, Imperial College London

Room 342

·         13:00-13:40 Emmanuel Essel (African Institute for Mathematical Sciences, Ghana) Reiterated homogenization applied in hydrodynamic lubrication

·         Coffee break

• 14:00-16:30 Melanie Rupflin (Oxford University, UK) Geometric flows and Plateau problem

Monday, 28 November, 3—4pm, Imperial College London

Room 341

·         15:00-15:40 Bakhtiyer Kadyrkulov (Tashkent State University for Oriental Studies, Uzbekistan)  On solvability of a nonlocal problem for the Laplace equation with the fractional-order boundary operator

·         Coffee break

## ABSTRACTS

Tsegaye Gedif Ayele (Addis Ababa University, Ethiopia) Analysis of two-operator boundary-domain integral equations for variable-coefficient mixed BVP

Abstract. Applying the two-operator approach, the mixed (Dirichlet-Neumann) boundary value problem for a second-order scalar elliptic differential equation with variable coeffcient is reduced to several systems of Boundary Domain Integral Equations, briefly BDIEs. The two-operator BDIE system equivalence to the boundary value problem, BDIE solvability and invertibility of the boundary-domain integral operators are proved in the appropriate Sobolev spaces.

Emmanuel Essel (African Institute for Mathematical Sciences, Ghana) Reiterated homogenization applied in hydrodynamic lubrication

Abstract. This work is devoted to studying the combined effect that arises due to surface texture and surface roughness in hydrodynamic lubrication. An effective approach in tackling this problem is by using the theory of reiterated homogenization with three scales. In the numerical analysis of such problems, a very fine mesh is needed, suggesting some type of averaging. To this end, a general class of problems is studied that, e.g. includes the incompressible Reynolds problem in both Cartesian and cylindrical coordinate forms. To demonstrate the effectiveness of the method several numerical results are presented that clearly show the convergence of the deterministic solutions towards the homogenized solution. Moreover, the convergence of the friction force and the load-carrying capacity of the lubricant film is also addressed in this paper. In conclusion, reiterated homogenization is a feasible mathematical tool that facilitates the analysis of this type of problem.

Mariano Rodriguez (University of Havana, Cuba) “Strong" Turing-Hopf instability for reaction-diffusion systems

Abstract. Turing instabilities and Hopf bifurcations often arise in mathematical models in a wide range of processes from developmental biology, ecology, chemistry, and technology. Introducing the concept of "Strong" Turing-Hopf instability for reaction-diffusion systems near a codimension two bifurcation point we pretend to model twinkling patterns. We focus on a normal mode approach for the study of diffusive instability, but in this case with reference to the instability of the stable limit cycle which emerges in a supercritical Hopf bifurcation. Some open questions.

Erkinjon Karimov (National University of Uzbekistan, Uzbekistan) Inverse-source non-local problem for mixed type equation with Caputo fractional differential operator



Abstract. In the present ​talk, we discuss a unique solvability of an inverse-source problem with integral transmitting condition for time-fractional mixed type equation in a rectangular domain, where the unknown source term depends on space variable only. The method of solution based on a series expansion using bi-orthogonal basis of space corresponding to a nonself-adjoint boundary value problem. Under certain regularity conditions on the given data, we prove ​a uniqueness and existence of the solution for the given problem. Influence of transmitting condition on the solvability of the problem is shown as well. Precisely, two different cases were considered; a case of full integral form ($0<\gamma<1$) and a special case ($\gamma=1$) of transmitting condition. In order to simplify the bulky expressions appearing in the proof of the main result, we have established a new property of the recently introduced Mittag-Leffler type function of two variables.

Stevan Pilipovic (University of Novi Sad, Serbia) Holder and Besov type regularities in Colombeau algebras of generalized functions

Abstract. Colombeau generalized functions contain distributions and all its subspaces. Every distribution is represented by a suitable regularized net consistinig of smooth functions parametrized by a parameter. Growth order with respect to the parameter determine essential properties of an embedded distributiion. In several papers we are studying embedded spaces of classical function spaces as Sobolev, Zigmund and Besov type spaces. This talk is devoted to the Tauberian type result with respect to regularization: To which space belongs an embedded distribution with respect to growth order with respect to the parameter? Joint work with jasson Vindas and Dimitris Scarpalezos.

Fikret Aliev (Institute of Applied Mathematics, Azerbaijan) Asymptotical methods for solutions of some identification problems

Abstract. The dynamic system, when the motion of the object is described by the system of nonlinear ordinary differential equations is considered. The right part of the system involves the phase coordinates as a unknown constant vector-parameter and a small number. The statistical data are taken from practice:  the initial and final values of the object coordinates. Using the method of quasilinearization the given equation is reduced to the system of linear differential equations, where the coefficients of the coordinate and unknown parameter, also of the perturbations  depend  on a small parameter linearly.Then, by using the least-squares method the unknown constant  vector-parameter is searched in the form of power series on a small parameter and for the coefficients of zero and the first orders the analytical formulas are given.  The fundamental matrices both in a zero and in the first  approaching are constructed approximately, by means of the ordinary Euler method. On an example of determination of the coefficient of hydraulic resistance (CHR) in the lift in the oil extraction by gas lift method is illustrated, as the obtained results in the first approaching  coincides with well-known results  on 10-2 order.

Fikret Aliev (Institute of Applied Mathematics, Azerbaijan) A method to determine the coefficient of hydraulic resistance in different areas of pump-compressor pipes

Abstract. In the work was consider mathematic model for defining hydraulic resistence coefficient  in the various part of the pump-compressor pipes in the oil wells operated by gaslift method. The multiparameter optimization problem by input-output parameters of the model was solved.

Bakhtiyer Kadyrkulov (Tashkent State University for Oriental Studies, Uzbekistan)  On solvability of a nonlocal problem for the Laplace equation with the fractional-order boundary operator

Abstract. We study an elliptic equation in a regular domain with a condition on the boundary involving a generalized Riemann-Liouville derivative of fractional order. The Bitsadze-Samarskii type problem is formulated for that equation. The uniqueness is proved by the maximum principle for harmonic functions. The Poisson kernel of the Dirichlet problem for the Laplace equation is used for proving the existence of a solution for the formulated problem.

For further information please contact
Michael Ruzhansky at this e-mail address


Suggestion of hotels in the area (Earl’s Court Station, 15 mins walk to Imperial College)

Merlyn Court Hotel
Maranton House Hotel
Barkston Gardens
City Hotel Kensington
For other hotels see here


How to get to the Department of Mathematics, Imperial College London

Travel to the tube station Gloucester Road (District, Circle, and Piccadilly Lines).

When you exit the station, turn left along Gloucester Road, crossing Cromwell Road 50 meters from the exit.

After 4-5 minutes walk along Gloucester Road, turn right to Queen's Gate Terrace.

This is a short road leading directly to the entrance of the Huxley Building, at 180 Queen's Gate. We are on floor 6.