Tatiana Savin

Recent News

Education

Ph.D., Lomonosov Moscow State University

Member

• Nanoscale & Quantum Phenomena Institute (NQPI)

Research Interests

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

Current Graduate Students

• Murdhy Aldawsari

Former Graduate Students

• Khalid Malaikah (Ph.D., 2013)
• Lanre Akinyemi (Ph.D., 2018)

Teaching

• 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).

Publications

• 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. (accepted in 2019).
• 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, 54 (2007) 733-740.
• T. V. Savina, A.A.Nepomnyashchy, and A.A.Golovin, "Delayed feedback control of rapid directional solidification " , J. Crystal Growth, 3072 (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.