
-
O. Costin, R. Donninger, I. Glogic and M. Huang, On the Stability of
Self-Similar Solutions to Nonlinear Wave Equations Comm. Math. Phys.,
343 (2016), no. 1, 299–310. CMP
-
O. Costin,
M.B. Gordy, M. Huang, P J Szerszen, Expectations of Functions of
Stochastic Time with Application to Credit Risk Modeling,
Mathematical Finance, vol. 26, no 4, pp 748--784. CMP
-
O. Costin,
N. Falkner, J D McNeal, Some generalizations of the
Riemann-Lebesgue lemma. Amer. Math. Monthly 123 (2016), no. 4,
387–391 MAA
-
O. Costin, R. D. Costin and M. Huang, A direct method to find Stokes
multipliers in closed form for P$ _1$ and more general integrable systems,
Trans. Amer. Math. Soc vol: 368 Issue: 11 pp:
7579-7621 (2016) (Dec 2015, online)
TAMS arXiv
-
O. Costin, P.
Ehrlich, H. Friedman, Integration on the Surreals: a
Conjecture of Conway, Kruskal and Norton, submitted, arXiv
- O. Costin, R. Donninger, I
Glogić, M. Huang, On the stability of self-similar solutions
to nonlinear wave equations, submitted,
arXiv
- O. Costin, R. Donninger, X.
Xia, A Proof for the Mode Stability of a Self-similar Wave
Map, Nonlinearity, V. 29, no. 8, pp. 2451--2473 arXiv
- O. Costin
and M. Huang, Decay estimates for One-dimensional wave
equations with inverse power potentials. Trans. Amer. Math.
Soc. 367 (2015) arXiv
- O. Costin, X. Xia, From
Taylor series of analytic functions to their global analysis,
Nonlinear Anal. 119 (2015), 106–114, arXiv
- O. Costin,
S. Tanveer, Analytical approximation of Blasius' similarity
solution with rigorous error bounds, SIAM J. Math. Anal. 46
(2014), no. 6, 3782–3813, arXiv
- O. Costin,
H. Friedman, Foundational aspects of singular integrals
Journal of Functional Analysis 267 (2014) 4732–4752. arXiv
-
O. Costin, M.
Huang Decay estimates for One-dimensional wave equations with
inverse power potentials, to appear in TAMS arXiv
- O. Costin,
T. Kim, S. Tanveer, A quasi-solution approach to nonlinear
problems - the case of Blasius similarity solution, Fluid Dyn.
Res. 46 (2014), no. 3, arXiv
-
-
O. Costin, M.
Huang and S. Tanveer, Proof of the Dubrovin conjecture and
analysis of the tritronquée solutions of $P_I$, Duke Math
Journal, 163, 4, pp. 665-704 (2014). arXiv
-
O. Costin,
R.D. Costin, M. Huang, Tronquee solutions of the Painleve
equation P1, Constr. Approx. 41 (2015), no. 3, 467–494. pdf
- O. Costin
and G. Giacomin, "Oscillatory Critical Amplitudes in
Hierarchical models and the Harris Function of Branching
Processes", J. Stat. Phys, 150, 3, pp 471--486 (2013).
arXiv
- O. Costin,
S. Tanveer, M. I. Weinstein, The lifetime of shape
oscillations of a bubble in an unbounded, inviscid and
compressible fluid with surface tension, SIAM J. Math. Anal.
45 (2013), no. 5, 2924–2936, arXiv
- O. Costin,
J. L. Lebowitz, G. Speer, A. Troiani, "The blockage problem",
Bull. Inst. Math. Acad. Sinica, Vol 8 no 1. (dedicated to SRS
Varadhan) (2013). arXiv
- O. Costin,
L. Dupaigne and O. Goubet, "Uniqueness of large solutions". J.
Math. Analysis and Applications, 395,2, pp. 806--812 (2012). arXiv
- Semiclassical
low energy scattering for one-dimensional Schrödinger
operators with exponentially decaying potentials (with R
Donninger, W Schlag and S Tanveer), Ann. Inst. Henri Poincaré , 13, 6, pp
1371--1426 (2012). .arXiv
- O. Costin, M Huang and W
Schlag, On the spectral properties of L± in
three dimensions Nonlinearity 25, pp. 125-164
(2012) arXiv
- O. Costin,
H. Parkh and Y. Takei, Borel summability of the heat equation
with variable coefficients, J. Diff. Eq. Volume 252, 4,
pp. 3076-3092 (2012).
- O. Costin,
M. Huang and F. Fauvet, Global behavior of solutions of
nonlinear ODEs: first order equations. Int Math Res
Notices first published online October 31, 2011
doi:10.1093/imrn/rnr203
- Gamow
vectors and Borel summability in a class of quantum systems
(with M Huang) J. Stat. Phys, Vol. 144, Number 4, pp. 846-871
(2011)
Springer link, free access
- Global
behavior of solutions of nonlinear ODEs: first order equations
(with M. Huang and F. Fauvet), submitted .arXiv
- Geometric
construction and analytic representation of Julia sets of
polynomial maps (with M. Huang) Nonlinearity 24 (2011), no. 4,
1311--1327 .arXiv
- Integral
equation representation and longer time existence solutions of
3-d Navier-Stokes (With G. Luo and S. Tanveer) Comm. Contemp.
Math, 13 (3), pp 407-462 (2011) ArXiv
- Boundary
blow-up solutions in the unit ball : asymptotics, uniqueness
and symmetry (with L. Dupaigne) J. Differential
Equations 249 (2010), no. 4, 931--964. arXiv
- Ionization of
Coulomb systems in ℝ3 by time periodic forcing
of arbitrary size (with J. L. Lebowitz and S.
Tanveer, Comm. Math. Phys. 296 (2010), no. 3,
681--738 Arxiv)
- Exact results for ionization of model
atomic systems (with J.L. Lebowitz, C. Stucchio
and S. Tanveer, J. Math. Phys., 51, 1 (2010). pdf
-
Resurgence of the fractional polylogarithms (with S.
Garoufalidis) , Math. Res. Lett. 16 (2009), no. 5,
817--82. arXiv
- Short time existence
and Borel summability in the Navier-Stokes equation in ℝ3
(with S. Tanveer). Comm. Partial Differential Equations 34
(2009), no. 7-9, 785--817 pdf
- Semiclassical
analysis
of low and zero energy scattering for one dimensional
Schrodinger operators with inverse square potentials
(with W. Schlag, W. Staubach, & S. Tanveer, J.
Functional Analysis, special issue dedicated to Paul
Malliavin, 255, (2008). arXiv
- Behavior of
lacunary series at the natural boundary (with M. Huang,
Advances in Mathematics 222 (2009) 1370–1404) Elsevier
link pdf
- Ionization
in damped harmonic fields (with M. Huang and Z. Qiu, J. Phys
A: Math. Theor, 42 (2009)) ArXiV link J.
Phys
A link
- An Integral equation Approach to Smooth 3-D Navier-Stokes
Solution (with G. Luo and S. Tanveer, Physica Scripta T 132,
2008).
- Resurgence of
the Euler-Maclaurin summation formula (with S.
Garoufalidis, Annales
de l' Institut Fourier 58 893-914 (2008) pdf
- Nonlinear Stokes phenomena in first or
second order differential equations (Algebraic
Analysis of Differential Equations, T. Aoki, H.
Majima, Y. Takei & N. Tose (Eds.), Springer
(2008)) pdf
- Ionization
in a 1-dimensional dipole model (with J. L. Lebowitz and
C. Stucchio), Reviews in Mathematical Physics, 20
No: 7 , pp. 835-872 (2008). pdf
- Sharp
Hardy-Leray inequality for axisymmetric divergence-free
fields (with V. Maz'ya,) Calc. Var. Partial
Differential Equations 32 (2008), no. 4,) pdf
- Divergent
expansions, Borel summability and the 3-D
Navier-Stokes Equation (With G. Luo and S. Tanveer, Phil.
Trans. R. Soc. A 366, pp 2775-2788 (2008)pdf.
- Resurgence
of the Kontsevitch-Zagier power series (with S.
Garoufalidis, to appear in Annales de l'Institut Fourier) pdf
- Global
reconstruction
of analytic functions from local expansions and a new
generalmethod of converting sums into integrals
(submitted) pdf
- On the
proof of universality for orthogonal and symplectic
ensembles in random matrix theory (with P. Deift
and D. Gioev J. Stat. Phys. 129 (2007), no. 5-6,
937--948) pdf
- Borel
summability and Lindstedt series (with G. Gallavotti, G.
Gentile and A. Giuliani, Comm. Math. Phys. v.269, 1;
175--193 (2007)) pdf
- Nonlinear evolution PDEs
in ℝ+×ℂd : existence and
uniqueness of solutions, asymptotics and Borel
summability (with S. Tanveer, Ann. Inst.
H. Poincaré Anal. Nonlin., 24, no. 5, pp. 795--823 (2007))
pdf
- Singularity
barriers
and Borel plane analytic properties of 1+
difference equations ( Recent Trends in Exponential
Asymptotics, Publ. RIMS 1424, (2005)) pdf
- Complex Singularity Analysis
for a nonlinear PDEs (with S
Tanveer, Comm. Partial Differential Equations 31, no.
4-6, 593--637 (2006)) pdf
- Analytic
methods
for obstruction to integrability in discrete dynamical
systems
(with M. Kruskal, Comm. Pure Appl. Math. 58
(2005), no. 6, 723--749) pdf
- Analyzable
functions
and Applications, AMS Contemporary Mathematics, vol
373
(with M. Kruskal and A. Macintyre
(editors))
- Topological construction of
transseries and introduction to generalized Borel
summability (AMS CONM series vol. 373,
137--177) pdf
- On the Construction of
Particle Distributions with Specified Single and
Pair Densities (with J. L.
Lebowitz, J. Phys. Chem. B.; 2004; 108(51);
19614-19618) pdf
- Analyzability
in the context of PDEs and applications
(with Saleh Tanveer; Annales Fac. Sci. Toulouse,
V XIII, Fasc. 4, pp.539--549 (2004); pdf
- Time asymptotics of the Schrödinger wave function in
time-periodic potentials (with R D
Costin and J L Lebowitz, J. Stat. Phys., special issue
dedicated to Elliott Lieb on the occasion of his 70th
birthday, 1--4 283-310 (2004). pdf
- Failure of analytic hypoellipticity
in a class of PDOs (with R. D.
Costin, Annali della Scuola Normale Superiore di Pisa,
Serie V. Vol II. Fasc. I (2003)) pdf
- Transition to the continuum
of a particle in time-periodic potentials, (with R. D. Costin and
J L Lebowitz in Advances in
Differential Equations and Mathematical Physics,
AMS Contemporary Mathematics series ed.
Karpeshina, Stolz, Weikard, and Zeng 2003)
pdf
- Borel summation of adiabatic
invariants (with L. Dupaigne and M.
D. Kruskal, Nonlinearity 17 No 4
1509-1519 (2004) ) pdf
- Rigorous bounds of Stokes
constants for some nonlinear ODEs at rank one
irregular singularities (with R.
D. Costin and M Kohut, Proc. R. Soc. Lond. A 460,
363--3641 (2004).) pdf
- Decay versus survival of a
localized state subjected to harmonic forcing: exact
results (with J L Lebowitz
and A Rokhlenko, J. Phys. A: Math. Gen. 35, pp 8943-8951
(2002)) pdf
- Movable singularities of
solutions of difference equations in relation to
solvability and a study of a superstable fixed point
(with M D Kruskal,
Theoretical and Mathematical Physics, 133 (2): 1455-1462
(2002)) .pdf
- Asymptotic properties of a
family of solutions of the Painleve equation PVI (with R D
Costin, IMRN No 22 pp 1167-1182 (2002)) .pdf
- On the formation of
singularities of solutions of nonlinear
differential systems in antistokes directions
(with R. D. Costin, Inventiones Mathematicae 145,
3, pp 425-485 (2001)) .pdf
(Copyright owned
by Inventiones)
- Evolution of a model quantum
system under time periodic forcing: conditions for
complete ionization (With R. D.
Costin, A. Rokhlenko and J. Lebowitz; Comm. Math.
Phys. 221, 1 pp 1-26 (2001)) pdf
- Existence and uniqueness of
solutions of nonlinear evolution systems of n-th
order partial differential equations in the complex plane (with
S. Tanveer) .pdf
- Resonance Theory for Schrödinger
Operators (with
A.
Soffer; Commun. Math. Phys. 224 (2001)) pdf
- Nonperturbative analysis of
a model quantum system under time periodic forcing
(With R. D. Costin, A. Rokhlenko and J. Lebowitz;
Comptes Rendus Acad. Sci. Serie I, 332 5 pp
405-411 (2001)) pdf
- Existence and uniqueness for
a class of nonlinear higher-order partial
differential equations in the complex plane
(with Saleh Tanveer. Communications on Pure and
Applied Mathematics, Vol. LIII, 0001- 0026 (2000)) pdf
- Exact Results for the
Ionization of a Model Quantum System
(with A. Rokhlenko and J. Lebowitz) J. Phys. A:
Math. Gen. 33 pp. 1--9 (2000) pdf
- On the complete ionization
of a periodically perturbed quantum system
(with A. Rokhlenko and J. Lebowitz) (CRM
Proceedings and Lecture Notes 27 pp 51--61
(2001)) pdf
- On optimal truncation of
divergent series solutions of nonlinear differential
systems; Berry smoothing. (with
Martin D. Kruskal, Proc. R. Soc. Lond. A 455,
1931-1956 (1999) .pdf
- Correlation between pole
location and asymptotic behavior for Painlevé I
solutions (Comm. Pure and
Appl. Math. Vol. LII, 0461-0478 (1999)) .ps.gz
.dvi.gz
- Singular normal form for the
Painleve equation P1 (with R. D.
Costin, Nonlinearity Vol 11, No. 5 pp.
1195-1208 (1998)) .pdf
- On Borel summation and
Stokes phenomena of nonlinear differential systems
( Duke Math. J. vol 93, No2 (1998)) .ps.gz
dvi.gz
- Optimal uniform estimates
and rigorous asymptotics beyond all orders for a
class of ODE's (with Martin D.
Kruskal, Proc. Roy. Soc. Lond. 452 (1996)) .ps.gz
- Rigorous WKB for finite
order linear recurrence relations with smooth
coefficients (with R.D. Costin,
SIAM.J.Math.Anal. v27 no1 (1996)) .ps.gz
(or abstract jpg
)
- Exponential asymptotics,
transseries, and generalized Borel summation for
analytic rank one systems of ODE's
(IMRN 8, (1995)) .ps.gz
- Gaussian fluctuations in
random matrices (with Joel
Lebowitz, Phys.Rev.Lett v 75 no 1 (1995)) pdf
- Limit probability
distributions for an infinite order phas transition
model J.
Stat.Phys.64 1/2 jpg
(abstract)
- Infinite order phase transition in a
classical spin system J. Stat.Phys.59 5/6 jpg
(abstract)
- The infinite coordinationl
limit for classical spin systems on irregular
lattices J. Phys. A:Math.Gen.19 jpg
(abstract)
Part of
the recent research was supported by the NSF awards
DMS-0103807, DMS-0100495, DMS-0406193, and DMS-0600369, DMS-1515755
and a Guggenheim fellowship.
Contact Information
-
Office: Math Tower 404
-
Telephone
(614) 292-7844
E-mail
Snail
Mail:
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Department
The Ohio State University
231 W. 18th Avenue
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