Tatiana Savin

Tatiana Savin a

Professor

Contact Information

Address:

Department of Mathematics

Office : 525 Morton Hall

Phone : 1-(740)-593-1268

E-mail : savin at ohio dot edu

Member
Nanoscale and Quantum Phenomena Institute (NQPI)

Ph.D . in Mathematics, Moscow University .

RESEARCH INTERESTS: analysis, partial differential equations, asymptotic methods, continuation of wave fields, wave propagation, mathematical modeling in materials science.

GRADUATE STUDENTS:

Caleb Siler (MS, 2025)

Khaled Qaraman (Ph.D., 2024)

Murdhy Aldawsari (Ph.D., 2022)

Suman Gautam (M.S., 2019)

Lanre Akinyemi (Ph.D., 2018)

Khalid Malaikah (Ph.D., 2013)

HTC STUDENTS:

Sierra Knavel (B.S., 2020)

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, https://doi.org/10.1051/mmnp/2019040 https://www.mmnp-journal.org/articles/mmnp/pdf/2020/01/mmnp190038.pdf .
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, ``OnDirichlet 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., 667 (2016), 199-210.
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'' , 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'' , 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.

Videos on PDE and Complex variables

www.youtube.com/@partialeducation6005

TEACHING:

Spring 2025: Math 6412 (Partial Differential Equations II), Math 4/5310 (Complex Variables), Math 7300 (Topics in Analysis), and Math 7400 (Topics in Differential Equations).
Fall 2024: Math 6411 (Partial Differential Equations I), Math 3300 (Calculus III), Math 7600 (Topics in Applied Mathematics), and Math 7400 (Topics in Differential Equations).
Spring 2024 Math 6412 (Partial Differential Equations II), Math 4/5310 (Complex Variables), Math 7300 (Topics in Analysis), and Math 8950 (dissertation).
Fall 2023: Math 6411 (Partial Differential Equations I), Math 8950 (dissertation), and Math 7400 (Topics in Differential Equations).
Spring 2023 Math 7300 (Topics in Analysis), and Math 8950 (dissertation).
Fall 2022: Math 8950 (dissertation).
Summer 2022: Math 5910 (internship).
Spring 2022: Math 6412 (Partial Differential Equations II), Math 7300 (Topics in Analysis), and Math 8950 (dissertation).
Fall 2021: Math 6411 (Partial Differential Equations I), Math 8950 (dissertation), Math 6930 (Number Theory), and Math 7400 (Topics in Differential Equations).
Summer 2021: Math 5910 (internship).
Spring 2021: Math 6412 (Partial Differential Equations II), Math 7300 (Topics in Analysis), and Math 8950 (dissertation).
Fall 2020: Math 6310 (Complex Analysis), Math 6411 (Partial Differential Equations I), and Math 8950 (dissertation).
Spring 2020: Math 4/5310 (Complex Variables), Math 4980T (Mathematics Tutorial, thesis), and Math 8950 (dissertation).
Fall 2019: Math 6310 (Complex Analysis), Math 3400 (Differential Equations), Math 4970T (Mathematics Tutorial, thesis), and Math 8950 (dissertation).
Summer 2019: Math 5910 (internship).
Spring 2019: Math 4/5310 (Complex Variables), Math 3980T (Junior Mathematics Tutorial), Math 7400 (Topics in Differential Equations), and Math 8950 (dissertation).
Fall 2018: Math 6310 (Complex Analysis), Math 2302 (Calculus II), Math 7400 (Topics in Differential Equations), and Math 8950 (dissertation).
Spring 2018: Math 4/5310 (Complex Variables), Math 6930 (Independent Study), Math 6942 (Project in Mathematics Education Research), and Math 8950 (dissertation).
Fall 2017: Math 6310 (Complex Analysis), Math 3400 (Differential Equations), Math 4310 (Complex variables), and Math 8950 (dissertation).
Spring 2017: Math 4/5310 (Complex Variables) and Math 8950 (dissertation).
Fall 2016: Math 3/5200 (Appl. Linear Algebra), Math 2301 (Calculus I), and Math 8950 (dissertation).
Spring 2016: Math 3/5320 (Vector Analysis), Math 4/5310 (Complex Variables) and Math 8950 (dissertation).
Fall 2015: Math 3/5200 (Appl. Linear Algebra), Math 6310 (Complex Analysis), Math 7300 (Topics in Analysis), and Math 8950 (dissertation).
Spring 2015: Math 3300 (Calculus III), Math 4/5310 (Complex Variables), and Math 7300 (Topics in Analysis).
Fall 2014: Math 7400 (Topics in Differential Equations).
Spring 2014: Math 3300 (Calculus III), Math 4/5310 (Complex Variables), Math 4940 (Mathematics Research).
Fall 2013: Math 2301 (Calculus I), Math 4/5400 (Advanced Differential Equations).
Summer 2013: Math 4310 (Complex Variables) and Math 3300 (Calculus III).
Spring 2013: Math 3/5320 (Vector Analysis), Math 4/5310 (Complex Variables), Math 8950 (dissertation).
Fall 2012: Math 1350 (Survey of Calc.), Math 3300 (Calculus III) and Math 8950 (dissertation).
Summer 2012: Math 895 (dissertation).
Spring 2012: Math 670C (Complex Analysis), Math 4/570 (Complex Variables), Math 741C , Math 692 .
Winter 2012: Math 670B (Complex Analysis) and Math 266B (Calc.Appl.Biology II), Math 741B , Math 692 .
Fall 2011: Math 670A (Complex Analysis) and Math 266A (Calculus with Applications to Biology I), Math 741A .
Summer 2011: Math 849 (Topics in Applied Mathematics) and Math 490 (Topics in Mathematics).
Spring 2011: Math 410/510 (Matrix Theory) and Math 263A (Calculus I).
Winter 2011: Math 340 (Differential Equations) and Math 263C (Calculus III).
Fall 2010: Math 340 (Differential Equations) and Math 410/510 (Matrix Theory).
Spring 2010: Math 4/570 (Complex Variables).
Winter 2010: Math 263B (Calculus II) and Math 263C (Calculus III).
Fall 2009: Math 4/540 (Vector Analysis) and Math 263C (Calculus III).
Spring 2009: Math 4/510 (Matrix Theory).
Winter 2009: Math 340 (Differential Equations) and Math 266A (Calculus with Applications to Biology I).
Fall 2008: Math 263A (Calculus I) and Math 263B (Calculus II).
Spring 2008: Math 4/510 (Matrix Theory).
Winter 2008: Math 340 (Differential Equations) and Math 266A (Calculus with Applications to Biology I).
Fall 2007: Math 340 (Differential Equations) and Math 263D (Calculus IV).
Spring 2007: Math 4/570 (Complex Variables) and Math 266B (Calculus with Applications to Biology II).
Winter 2007: Math 263A (Calculus I) and Math 266A (Calculus with Applications to Biology I).
Fall 2006: Math 4/540 (Vector Analysis) and Math 690 (Complex Analysis).

Last Modified: July 9, 2025

Tatiana Savina

Contact Information:

(740) 593–9381 | Building 21, The Ridges

Ohio University Contact Information:

Ohio University

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