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Computational Mathematics


Computational Mathematics

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ANH-KHOA VO


Nonlinear partial differential equations

  • Analysis: weak solvability, qualitative properties of weak solutions (positivity, decay and blow-up profiles)
  • Multiscale problems: homogenization (asymptotic expansions, macroscopic reconstruction), perforated domains, corrector estimates
  • Inverse problems: regularization (quasi-reversibility, quasi-boundary value, truncation), stability, error estimates
  • Age/size-structured problems: linearization schemes, rates of convergence

Personal

Born on October 12, 1992 in Ho Chi Minh City, Vietnam
Married with Thi Kim Ngan Huynh
Languages: Vietnamese (mother’s), English

Employment

Oct. 2018 – present: Postdoctoral fellow at Hasselt University, Research group Computational mathematics (led by Prof. Dr. Iuliu Sorin Pop)
Feb. 2018 – Aug. 2018: Postdoctoral researcher at NAM, University of Göttingen, Research group Inverse problems (led by Prof. Dr. Thorsten Hohage)

Fellowships and grants

Oct. 2018 – Oct. 2021: Approximations for forward and inverse reaction- diffusion problems related to cancer models, Postdoctoral fellowship (PI) by Research Foundation - Flanders (FWO)
Jul. 2014 – Aug. 2014: Travel grant by Institute for Advanced Study in Mathematics, Hanoi, Vietnam

Awards

2018: Outstanding Reviewer of 2017 for the journal Inverse Problems
2013 – 2014: Scholarship of National Program for the Development of Mathematics
2010 – 2020, Vietnam Institute for Advanced Study in Mathematics
2009: Bronze medal in the 30th-April Olympiad Competition in Mathematics in Vietnam

Education

Nov. 2014 – Jan. 2018: Ph’D degree in Mathematics (Cum Laude, 110/110), Gran Sasso Science Institute (L’Aquila) and Scuola Internazionale Superiore diStudi Avanzati (Trieste), Italy
Thesis: Corrector Homogenization Estimates for PDE Systems with Coupled Fluxes posed in Media with Periodic Microstructures (defense date: January 16, 2018)
Advisor: Prof. Dr. habil. Adrian Muntean (Karlstad University, Sweden)
Oct. 2010 – Oct. 2014: Bachelor degree in Mathematics and Computer Science (Distinction – 5%, Honor program), University of Science, Vietnam National University, Ho Chi Minh City, Vietnam
Thesis: Linear recursive and second-order iterative schemes for a nonlinear Kirchhoff wave equation associated with the mixed homogeneous boundary conditions (defense date: March 24, 2014)
Advisor: Dr. Nguyen Thanh Long (University of Science, Vietnam), Dr. Tran Minh Thuyet (University of Economics, Vietnam)

List of publications 

Refereed journal publications:

  1. V.A. Khoa, L.T.P. Ngoc, N.T. Long, Existence, blow-up and exponential decay of solutions for a porous-elastic system with damping and source terms, accepted for publication in Evolution Equations & Control Theory, 2018 (also see CMAT Report UP-18-08, Hasselt University).
  2. N.H. Tuan, V.A. Khoa, M.T.N. Truong, T.T. Hung, M.N. Minh, Application of the cut-off projection to solve a backward heat conduction problem in a two-slab composite system, accepted for publication in Inverse Problems in Science and Engineering, 2018.
  3. N.H. Tuan, V.V. Au, V.A. Khoa, D. Lesnic, Identification of the population density of a species model with nonlocal diffusion and nonlinear reaction, Inverse Problems, 33 (5), 2017.
  4. V.N. Doan, H.T. Nguyen, V.A. Khoa, V.A. Vo, A note on the derivation of filter regularization operators for nonlinear evolution equations, Applicable Analysis, 97 (1): 3–12, 2017.
  5. V.A. Khoa, A high-order corrector estimate for a semi-linear elliptic system in perforated domains, Comptes Rendus M ́ecanique, 345 (5): 337--343, 2017.
  6. V.A. Khoa, T.T. Hung, Regularity bounds for a Gevrey criterion in a kernel-based regularization of the Cauchy problem of elliptic equations, Applied Mathematics Letters, 69: 75–81, 2017.
  7. N.H. Tuan, V.A. Khoa, M.N. Minh, T. Tran, Reconstruction of the electric field of the Helmholtz equation in three dimensions, Journal of Computational and Applied Mathematics, 309: 56–78, 2017.
  8. V.A. Khoa, M.T.N. Truong, N.H.M. Duy, N.H. Tuan, The Cauchy problem of coupled elliptic sine-Gordon equations with noise: Analysis of a general kernel-based regularization and reliable tools of computing, Computers & Mathematics with Applications, 73 (1): 141–162, 2016.
  9. V.A. Khoa, A. Muntean, A note on iterations-based derivations of high-order homogenization correctors for multiscale semi-linear elliptic equations, Applied Mathematics Letters, 58: 103–109, 2016.
  10. V.A. Khoa, A. Muntean, Asymptotic analysis of a semi-linear elliptic system in perforated domains: Well-posedness and correctors for the homogenization limit, Journal of Mathematical Analysis and Applications, 439 (1): 271–295, 2016.
  11. V.T. Nguyen, H.T. Nguyen, T.B. Tran, A.K. Vo, On an inverse problem in the parabolic equation arising from ground water pollution problem, Boundary ValueProblems, 2015:67, 2015.
  12. N.H. Tuan, L.D. Thang, V.A. Khoa, A modified integral equation method of the nonlinear elliptic equation with globally and locally Lipschitz source, Applied Mathematics and Computation, 265: 245–265, 2015.
  13. V.A. Khoa, T.N. Huy, L.T. Lan, N.T.Y. Ngoc, A finite difference scheme for nonlinear ultra-parabolic equations, Applied Mathematics Letters, 46: 70–76, 2015.
  14. N.H. Tuan, V.A. Khoa, L.T. Lan, T.T. Hung, On the regularization of solution of an inverse ultraparabolic equation associated with perturbed final data, Journal of Inequalities and Applications, 2015:13, 2015.
  15. N.H. Tuan, L.D. Thang, D.D. Trong, V.A. Khoa, Approximation of mild solutions of the linear and nonlinear elliptic equations, Inverse Problems in Science and Engineering, 23 (7): 1237–1266, 2015.
  16. N.H. Tuan, L.D. Thang, V.A. Khoa, T. Tran, On an inverse boundary value problem of nonlinear elliptic equation in three dimensions, Journal of Mathematical Analysis and Applications, 426 (2): 1232–1261, 2014.
  17. N.H. Tuan, B.T. Duy, N.D. Minh, V.A. Khoa, H ̈older stability for a class of initial inverse nonlinear heat problem in multiple dimension, Communications in Nonlinear Science and Numerical Simulation, 23 (1–3): 89–114, 2014.

Preprints:

  1. V.A. Khoa, T.T. Hung, D. Lesnic, Uniqueness result for an age-dependent reaction-diffusion problem, CMAT Report UP-18-07, Hasselt University, 2018.
  2. V.A. Khoa, T.T.K. Thoa, E.R. Ijioma, On a pore-scale stationary diffusion equation: scaling effects and correctors for the homogenization limit, arXiv:1803.10887, 2018.
  3. N.H. Tuan, V.A. Khoa, V.V. Au, Analysis of a quasi-reversibility method for a terminal value quasi-linear parabolic problem with measurements, arXiv:1803.04641, 2018.
  4. V.A. Khoa, A. Muntean, Correctors homogenization estimates for a non-stationary Stokes-Nernst-Planck-Poisson system in perforated domains, arXiv:1710.09166, 2017.
  5. V.A. Khoa, A. Muntean, Correctors justification for a Smoluchowski-Soret-Dufour model posed in perforated domains, arXiv:1704.01790, 2017.

Book contributions and proceedings:

  1. V.A. Khoa, L.T.P. Ngoc, N.T. Long, Existence, blow-up and exponential decay of solutions for a nonlinear porous-elastic system, The Eleventh Scientific Conference of University of Science, Vietnam National University Ho Chi Minh City, 2018.