Tatiana Savin

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Education

Ph.D., Lomonosov Moscow State University

About Tatiana Savin

Tatiana Savin is a professor of mathematics and an NQPI member at Ohio University.

She joined Ohio University in 2006 as an assistant professor of mathematics. She was promoted to associate professor in 2012 and to professor in 2019. Throughout her time at Ohio University, she served in multiple different positions including Graduate Chair of Math. Department (2016-2022) and NSF review panelist in the Division of Mathematical Sciences (2008).

Dr. Savin enjoys teaching, research, and other scientific communications with students. Due to her dedication to her students, she won the 2017-18 Jeanette Grasselli Brown Faculty Teaching Award in Natural Sciences/Mathematics.

Prior to coming to Ohio University, Dr. Savin also served in several other positions related to mathematics, physics, and engineering. Dr. Savin was a J. Ford fellow in the School of Physics at Georgia Institute of Technology and a visiting scholar in the Department of Engineering Sciences and Applied Mathematics at Northwestern University. While at Northwestern, Dr. Savin worked on an NSF Nanoscale Interdisciplinary Research Team. 

Research Interests

• Applied analysis
• Analytic continuation of solutions to elliptic differential equations
• Partial differential equations
• Mathematical modeling in materials science

Thesis Directed

• Khaled Qaraman, ``On inversion in higher dimensions”, Ph.D., Spring 2024.
• Murdhy Aldawsari, ``On Non-homogeneous Reflections via Dirichlet-to-Neumann and Robin-to-Neumann Operators”, Ph.D., Fall 2022.
• Sierra Knavel, ``The high-order Cahn-Hilliard type model for the solid-state dewetting of a thin film'', HTC, B.S., Spring 2020.
• Suman Gautam, ``On the geometric properties of the Schwarz function”, M.S., Fall 2019.
• Lanre Akinyemi, ``The interface dynamics in the Hele-Shaw cell”, Ph.D., Spring 2018.
• Khalid Malaikah, ``Laplacian growth: interface evolution in a Hele-Shaw cell'', Ph.D., Spring 2013.

Teaching

• Videos on PDE and Complex variables 

Publications

• M. Aldawsari and T. Savina ``On non-homogeneous Robin reflection for harmonic functions”, Applicable Analysis, 101, Issue 5, (2022), 1699-1714.
• T.V. Savina, ``On a two-fluid Hele-Shaw problem with an elliptical interface”, J. Differential Equations, 270 (2021), 787-808.
• S.A. Knavel, T.V.  Savina, M.V. Mroz, M.E. Kordesch, C.N Eads, J.T. Sadowski, and S.A. Tenney, ``A mathematical model of solid-state dewetting of barium thin films on W(112)'',  Math. Model. Nat. Phenom., 15 (2020) 12.
• T. Savina,  "From reflections to a uniform elliptic growth", Journal of Mathematical Analysis and Applications, 447 (2019), issue 2, 1419-1433.
• M. Aldawsari and T. Savina, "On  Dirichlet to Neumann and Robin to Neumann operators suitable for reflecting harmonic functions subject to a non-homogeneous condition on an arc,"  Analysis and Mathematical Physics, 9,  (2019), no. 2, 729-745.
• M.V. Mroz, T. Savina, M.E. Kordesch, J.T. Sadowski, and S.A. Tenney, "Solid-solid dewetting of scandium thin films on the W(100) surface observed using emission microscopy", JVST B,  37, (2019), 012903; doi: 10.1116/1.5066015
• M. Mroz, S. Tenney, T. Savina, and M.E. Kordesch, "Thermionic emission microscopy of scandium thin film dewetting on W(100)", AIP Advances,  8, (2018), 065114; doi: 10.1063/1.5039612.
• T. Savina, L. Akinyemi, and A. Savin, "On a two-phase Hele-Shaw problem with a time-dependent gap and distributions of sinks and sources"', Journal of Physics A: Mathematical and Theoretical, 51 (2018), no. 4, 045501 (16pp).
• L. Akinyemi, T. V. Savina and A.A. Nepomnyashchy, "Exact solutions to a Muskat problem with line distributions of sinks and sources", Contemporary Math., 699 (2017), 19-33.
• K. Malaikah, T. V. Savina and A.A. Nepomnyashchy, "Hele-Shaw flow with a time-dependent gap: the Schwarz function approach to the interior problem", Contemporary Math., 2 (2016), to appear.
• T. V. Savina and A.A. Nepomnyashchy, "The shape control of a growing air bubble in a Hele-Shaw cell", SIAM J. Appl. Math., 75 (2015), no. 3, 1261–1274.
• T. V. Savina and A.A. Nepomnyashchy, "On a Hele-Shaw flow with a time-dependent gap in the presence of the surface tension", Journal of Physics A: Mathematical and Theoretical, 48 (2015), no. 12, 125501 (13pp).
• T. Savina, "On non-local reflection for elliptic equations of the second order in R^2 (the Dirichlet condition)'", Transactions of the American Mathematical Society, 364 (2012), no. 5, 2443-2460.
• T. V. Savina and A.A. Nepomnyashchy, "A dynamical mother body in a Hele-Shaw problem", Physica D, 240 (2011), 1156-1163.
• T.V. Savina, "On the dependence of the reflection operator on boundary conditions for biharmonic functions", Journal of Mathematical Analysis and Applications, 370 (2010), 716-725.
• T.V. Savina, "On the structure of the reflection formula for the biharmonic equation", in: 7th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, S. Sivasundaram, editor, Cambridge Scientific Publishers, (2009).
• B.P. Belinskiy and T.V. Savina, "The Schwarz reflection principle for harmonic functions in R^2 subject to the Robin condition", Journal of Mathematical Analysis and Applications, 348 (2008), 685-691.
• T.V.Savina, "On splitting up singularities of fundamental solutions to elliptic equations in C^2", Central European Journal of Mathematics, 5 4 (2007) 733-740.
• T. V. Savina, A.A.Nepomnyashchy, and A.A.Golovin, "Delayed feedback control of rapid directional solidification", J. Crystal Growth, 307 2 (2007), 490-499.
• T.V. Savina, B.Yu.Sternin and V.E.Shatalov, "On a minimal element for a family of bodies producing the same external gravitational field", Applicable Analysis 84, (2005), no. 7, 649-668.
• A.A.Golovin, M.S.Levine, T.V.Savina and S.H.Davis, "Faceting instability in the presence of wetting interactions: a mechanism for the formation of quantum dots" [PDF], Phys. Rev. B 70, (2004), no. 23, 235342, 11 p.
• T.V.Savina, P.W.Voorhees and S.H.Davis, "The effect of surface stress and wetting layers on morphological instability in epitaxially strained films" J. Appl. Phys. 96, (2004), no. 6, 3127-3133.
• T.V.Savina, A.A.Golovin, S.H.Davis, A.A.Nepomnyashchy and P.W.Voorhees, "On faceting of a growing crystal surface by surface diffusion", Physical Review E 67, 021606, (2003), 1-16.
• T.V.Savina, A.A.Nepomnyashchy, S.Brandon, D.R.Lewin and A.A.Golovin, "Suppressing morphological instability via feedback control", Journal of Crystal Growth, 240 (2002), 292-304.
• T.Savina, A.A.Nepomnyashchy, S.Brandon, A.A.Golovin and D.R.Lewin, "Feedback control of morphological instability", J. Crystal Growth 237-239 (2002), 178-180.
• D.Aberra and T.Savina, "The Schwarz reflection principle for polyharmonic functions in R^2'', Complex Variables Theory Appl. 41 (2000), no 1, 27-44.
• T.V.Savina, "A reflection formula for the Helmholtz equation with the Neumann condition" [PDF], Comput. Math. Math. Phys. 39 (1999), no. 4, 652-660.
• T.V.Savina, "On a reflection formula for higher-order elliptic equations'' , Math. Notes 57 (1995), no. 5-6, 511-521.
• T.V.Savina, B.Yu.Sternin and V.E.Shatalov, "On the continuation of solutions in domains with a piecewise-analytic boundary", (Russian), Dokl. Akad. Nauk 341 (1995), no. 1, 24-27.
• T.V.Savina, "On the law of reflection for higher-order elliptic equations", Russian Acad. Sci. Dokl. Math. 48 (1994), no. 2, 380-383.
• T.V.Savina, B.Yu.Sternin and V.E.Shatalov, "On the reflection formula for the Helmholtz equation" (Russian), Radiotekh. i Electron. 38 (1993), no. 2, 229--240.
• T.V.Savina, B.Yu.Sternin and V.E.Shatalov, "On the reflection law for the Helmholtz equation", Soviet Math. Dokl. 45 (1992), no.1, 42-45.
• N.A.Kudryashov and T.V.Savina, "Invariant solutions of an equation of gas filtration in a porous medium for large Reynolds numbers" (Russian), Mat. Model. 2 (1990), no. 12, 122-126.

Book Chapter

• T.V.Savina, B.Yu.Sternin and V.E.Shatalov, "Reflection Formulas and Continuation of Solutions to Boundary Value Problems", Section in the book: Boris Sternin and Victor Shatalov, Differential Equations on Complex Manifolds, Kluwer Academic Publishers, Dordeht-Boston-London, 1994.

Preprints

• T.V.Savina, B.Yu.Sternin and V.E.Shatalov, "Notes on mother body in geophysics'" Preprint Max-Plank Institut fur Mathematik, Bonn, MPI/95-90, 23 p.