Alexander Panchenko

Partial Differential Equations and Applied Mathematics
Homogenization $\bullet$ Fluid-Particle Flows $\bullet$ Acoustic Wave Propagation
Biological Tissue Modeling $\bullet$ Inverse Problems

1. Quasi-exponential solutions for some PDE with coefficients of limited regularity. In: Direct and inverse problems of mathematical physics, Kluwer, Dordrecht, (2000) 161-184.

2. The exponential X-Ray transform and John's Equation. I. Range description (with L. Ehrenpreis and P. Kuchment), Contemporary Mathematics, 251 (2000), 173-188.

3. On a differential operator containing a large complex parameter. Applicable Analysis, 74 (2000), 1-26.

4. An inverse problem for the magnetic Schroedinger Equation and quasi-exponential solutions of nonsmooth partial differential equations. Inverse Problems, 18(5) (2002), 1421-1434.

5. Vibration of two bonded periodic composites (with V. Harik and R. P. Gilbert), International Journal of Solids and Structures, 40(12) (2002), 3177-3193.

6. Effective acoustic equations for a nonconsolidated medium with microstructure (with R. P. Gilbert), In: Acoustics, mechanics and the related topics of mathematical analysis, World Scientific, River Edge, NJ, (2002), 164-170.

7. Complex geometrical optics solutions for Lipschitz conductivity (with L. Paivarinta and G. Uhlmann), Revista Matematica Iberoamericana, 19 (2003), 56-72.

8. Effective acoustic equations of a two-phase medium with microstructure (with R. P. Gilbert), Mathematical and Computer Modelling, 39(13) (2004), 1431-1448.

9. Network approximation for effective viscosity of highly concentrated suspensions with complex geometry (with L. Berlyand, and L. Borcea), SIAM Journ. Math. Analysis, 36(5) (2005), 1580-1628.

10. Homogenization of a viscoelastic matrix in linear frictional contact (with R. P. Gilbert and X. Xie), Math. Models and Methods in Applied Sciences, 28 (2005), 309-328.

11. Strong and weak blow up of the viscous dissipation rates for concentrated suspensions (with L. Berlyand), Journal of Fluid Mechanics, 578 (2007), 1-34.

12. Young measures and order-disorder transition in liquid crystal flows (with M. C. Calderer), SIAM Journ. Math. Analysis. (Accepted.)
    Preprint available at http://www.math.wsu.edu/math/faculty/panchenko.

13. A prototype homogenization model for acoustics of granular materials (with R. P. and X. Xie), International Journal of Multiscale Computational Engineering, 4, (5-6), (2006), 585-600.

14. A network model of geometrically constrained deformations of granular materials (with K. A. Ariyawansa and L. Berlyand), Networks and Heterogeneous Media. (Accepted.)
    Preprint available at http://www.math.wsu.edu/math/faculty/panchenko.

15. Homogenizing the time harmonic acoustics of bone: the monophasic case (with M. Fang, R. P. Gilbert and A. Vasilic), Mathematical and Computer Modeling. (Accepted).