Achenef Tesfahun
Position:
PhD Norwegian University of Science and Technology
Assistant Professor
Assistant Professor
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Research Interest
My main research interest is in the analysis of Partial Differential Equations with a particular focus on the study of low regularity well-posedness and long-time behavior of solutions to nonlinear dispersive and wave equations arising from quantum and fluid mechanics. Harmonic analysis techniques are central in my research.
Biography
Selected Publications
Courses Offered
| Education | Ph.D in Mathematics Norwegian University of Science and Technology |
2009 Norway |
| Master in Mathematics Norwegian University of Science and Technology |
2003 Norway |
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| Bachelor in Mathematics (minor in Statistics) Adis Abeba University |
2000 Ethiopia |
- A. Tesfahun, Small data scattering for cubic Dirac equation with Hartree type nonlinearity in R1+3. To appear in SIAM J. Math. anal.
- S. Selberg, A. Tesfahun, Ill-posedness for the Thirring model below the critical regularity. J. Math. Phys. 61 071504 (2020): doi: 10.1063/1.5124096
- D. Evgueni, S. Selberg, A. Tesfahun, Well-posedness for a dispersive system of the Whitham-Boussinesq type. SIAM J. Math. Anal. 52 (3), 2353–2382.
- A. Tesfahun, On the growth of higher order Sobolev norms of solutions to the 1D Dirac-Klein-Gordonsystem. J.Hyp.Diff.Equations 16(2019)1–20. DOI: 10.1142/S0219891619500127
- A. Tesfahun, Remarks on the persistence of spatial analyticity for cubic nonlinear Schrödinger equation on the circle. Nonlinear Differ. Equ. Appl. (2019) 26:12. DOI.org/10.1007/s00030-019-0558-6
- A. Tesfahun, Asymptotic lower bound for the radius of spatial analtyicity to solutions of KdV equation. Communications in Partial Differential Equations, doi.org/10.1142/S021919971850061X
- A. Tesfahun, Long-time Behavior of Solutions to Cubic Dirac Equation with Hartree Type Nonlinearity in R1+2. Int. Math. Res. Notices (2018): doi.org/10.1093/imrn/rny217.
- S. Selberg, A. Tesfahun, On the radius of spatial analyticity for the quartic generalized KdV equation. Ann. Henri Poincare 18 (2017), no. 11, 3553–3564: DOI 10.1007/s00023-017-0605-y
- A. Tesfahun, Lower bound for the radius of spatial analyticity for the cubic nonlinear Schrödinger equation. J. Differential Equations 263 (2017) 7496–7512
- S. Selberg, A. Tesfahun, Null structure and local well-posedness in the energy class for the Yang-Mills equations in Lorenz gauge. J. Eur. Math. Soc. 18(2016),1729-1752
- A. Tesfahun, Local well-posedness of the Yang-Mills equations in Lorenz gauge below the energy norm. Nonlinear Differ. Equ. Appl. 22 (2015), 849-875
- S. Herr, A. Tesfahun, Small data scattering for semi-relativistic equations with Hartree type nonlinearity. J. Differential Equations 259 (2015) 5510-5532
- S. Selberg, A. Tesfahun, On the radius of spatial analyticity for the 1D DiracKlein-Gordon Equations. J. Differential Equations 259 (2015) 4732-4744
- A. Tesfahun, Finite energy local well-posedness for the Yang-Mills-Hills equations in Lorenz gauge. Int. Math. Res. Notices (2015): doi.org/10.1093/imrn/rnu087.
- A. Tesfahun, Almost optimal local well-posedness for the space-time monopole equation in Lorenz gauge. Commun. Contemp. Math., 17, 1450043 (2015)
- S. Selberg, A. Tesfahun, Global well-posedness of the Chern-Simons-Higgs equations with finite energy. Discrete and Continuous Dynamical Systems, 33 (2013) 2531–2546.
- S. Selberg, A. Tesfahun, Unconditional uniqueness in the charge class for the Dirac-Klein-Gordon equations in two space dimensions. (With S.Selberg). Nonlinear Differ.Equ.Appl.20(2013), 1055-1063
- S. Selberg, A. Tesfahun, Finite-energy global well-posedness of the MaxwellKlein-Gordon equations in Lorenz gauge. (With S. Selberg). Communications in Partial Differential Equations, 35 (2010), 1029-1057.
- S. Selberg, A. Tesfahun, Remarks on regularity and uniqueness of the one dimensional Dirac-Klein-Gordon equations. Nonlinear Differ. Equ. Appl. 17 (2010) 453-465
- S. Selberg, A. Tesfahun, Low regularity well-posedness for some nonlinear Dirac equations in one space dimension. Differential Integral Equations 23 (2010), 265-278.
- S. Selberg, A. Tesfahun, On the Maxwell-Klein-Gordon equations in Lorenz gauge. (With S. Selberg). Proceedings of the International Congress of Mathematical Physics (2009).
- A. Tesfahun, Global Well-posedness of the 1D Dirac-Klein-Gordon system in Sobolev spaces of negative index. J. Hyper. Differential Equations, 06, 631 (2009).
- A. Tesfahun, Low regularity and local well-posedness for the 1+3 dimensional Dirac-Klein- Gordon system. Electronic J. Differential Equations 2007 (2007), 1–26
- S. Selberg, A. Tesfahun, Low regularity well-posedness of the Dirac-KleinGordon system in one space dimension. Commun. Contemp. Math., 10 (2008) 181-194
- MATH 161 – Calculus I
- MATH 676 – Advanced PDEs with Applications
