Vanja Nikolić

Vanja Nikolić

Assistant Professor at Radboud University

 
Preprints
 
 
Journal articles
 
  1. V. Nikolić: Asymptotic-preserving finite element analysis of Westervelt-type wave equations, Anal. Appl., to appear. [arxiv]
  2. P. Manns and V. Nikolić: Homotopy trust-region method for phase-field approximations in perimeter-regularized binary optimal control, ESAIM: COCV, to appear. [arxiv]
  3. B. Cox, B. Kaltenbacher, V. Nikolić, and F. Lucka: Existence of solutions to k-Wave models of nonlinear ultrasound propagation in biological tissue, Stud. Appl. Math., 153(4): e12771. [arxiv]
  4. V. Nikolić and M. Winkler: L∞ blow-up in the Jordan–Moore–Gibson–Thompson equation, Nonlinear Analysis, 247: 113600, 2024. [arxiv]
  5. B. Kaltenbacher, M. Meliani, and V. Nikolić: Limiting behavior of quasilinear wave equations with fractional-type dissipation, Adv. Nonlinear Stud., 4(3): 748–774, 2024. [arxiv]
  6. B. Kaltenbacher, M. Meliani, and V. Nikolić: The Kuznetsov and Blackstock equations of nonlinear acoustics with nonlocal-in-time dissipation, Appl. Math. Opt., 89(3): 1-37, 2024. [arxiv]
  7. V. Nikolić: Nonlinear acoustic equations of fractional higher order at the singular limit, Nonlinear Differ. Equ. Appl. NoDEA, 31(3): 30, 2024. [arxiv]
  8. M. Meliani and V. Nikolić: Mixed approximation of nonlinear acoustic equations: Well-posedness and a priori error analysis, Applied Numerical Mathematics, 198: 94-111, 2024. [arxiv] [code]
  9. B. Kaltenbacher and V. Nikolić: The vanishing relaxation time behavior of multi-term nonlocal Jordan–Moore–Gibson–Thompson equations, Nonlinear Anal. Real World Appl., 76, 2024. [arxiv]
  10. V. Nikolić and B. Said-Houari: Time-weighted estimates for the Blackstock equation in nonlinear ultrasonics, J. Evol. Equ., 23(3): 59, 2023. [arxiv]
  11. V. Nikolić and B. Said-Houari: Local well-posedness of a coupled Westervelt–Pennes model of nonlinear ultrasonic heating, Nonlinearity, 35(11): 5749, 2022. [arxiv]
  12. M. Meliani and V. Nikolić: Analysis of general shape optimization problems in nonlinear acoustics, Appl Math Optim, 86(3): 39, 2022. [arxiv]
  13. V. Nikolić and B. Said-Houari: The Westervelt–Pennes model of nonlinear thermoacoustics: Global solvability and asymptotic behavior, J. Differ. Equat., 336: 628–653, 2022.
  14. B. Kaltenbacher, U. Khristenko, V. Nikolić, M. L. Rajendran, and B. Wohlmuth: Determining kernels in linear viscoelasticity, J. Comput. Phys., 464: 2022. [arxiv]
  15. H. Garcke, S. Mitra, and V. Nikolić: A phase-field approach to shape and topology optimization of acoustic waves in dissipative media, SIAM J. Control Optim., 60(4): 2297–2319, 2022. [arxiv]
  16. B. Kaltenbacher and V. Nikolić: Time-fractional Moore–Gibson–Thompson equations, Math. Models Methods Appl. Sci., 32(5): 965–1013, 2022. [arxiv]
  17. B. Kaltenbacher and V. Nikolić: Parabolic approximation of quasilinear wave equations with applications in nonlinear acoustics, SIAM J. Math. Anal., 54(2): 2022. [arxiv]
  18. M. Muhr, V. Nikolić, and B. Wohlmuth: A discontinuous Galerkin coupling for nonlinear elasto-acoustics, IMA J. Numer. Anal., 43(1): 225-257, 2023. [arxiv]
  19. V. Nikolić and B. Said-Houari: Asymptotic behavior of nonlinear sound waves in inviscid media with thermal and molecular relaxation, Nonlinear Anal. Real World Appl., 62: 103384, 2021. [arxiv]
  20. B. Kaltenbacher and V. Nikolić: The inviscid limit of third-order linear and nonlinear acoustic equations, SIAM J. Appl. Math., 81(4): 1461–1482, 2021. [arxiv]
  21. V. Nikolić and B. Said-Houari: Mathematical analysis of memory effects and thermal relaxation in nonlinear sound waves on unbounded domains, J. Differ. Equat., 273: 172-218, 2021. [arxiv]
  22. V. Nikolić and B. Said-Houari: On the Jordan–Moore–Gibson–Thompson wave equation in hereditary fluids with quadratic gradient nonlinearity, J. Math. Fluid Mech., 23: 1-24, 2021. [arxiv]
  23. P. F. Antonietti, I. Mazzieri, M. Muhr, V. Nikolić, and B. Wohlmuth: A high-order discontinuous Galerkin method for nonlinear sound waves, J. Comput. Phys., 415: 109484, 2020. [arxiv]
  24. B. Kaltenbacher and V. Nikolić: Vanishing relaxation time limit of the Jordan–Moore–Gibson–Thompson wave equation with Neumann and absorbing boundary conditions, Pure Appl. Funct. Anal.: Special issue dedicated to Prof. Irena Lasiecka, 5(1): 1-26, 2020. [arxiv]
  25. M. Fritz, E. A.B.F. Lima, V. Nikolić, J. T. Oden, and B. Wohlmuth: Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation, Math. Models Methods Appl. Sci., 29(13): 2433–2468, 2019. [arxiv]
  26. V. Nikolić and B. Wohlmuth: A priori error estimates for the finite element approximation of Westervelt's quasilinear acoustic wave equation, SIAM J. Numer. Anal., 57(4): 1897–1918, 2019. [arxiv]
  27. B. Kaltenbacher and V. Nikolić: The Jordan–Moore–Gibson–Thompson equation: Well-posedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time, Math. Models Methods Appl. Sci., 29(13): 2523–2556, 2019. [arxiv]
  28. M. Muhr, V. Nikolić, and B. Wohlmuth: Self-adaptive absorbing boundary conditions for quasilinear acoustic wave propagation, J. Comput. Phys., 388: 279–299, 2019. [arxiv]
  29. M. Muhr, V. Nikolić, B. Wohlmuth, and L. Wunderlich: Isogeometric shape optimization for nonlinear ultrasound focusing, Evol. Equ. & Control Theory, 8(1): 163–202, 2019. [arxiv]
  30. M. Fritz, V. Nikolić, and B. Wohlmuth: Well-posedness and numerical treatment of the Blackstock equation in nonlinear acoustics, Math. Models Methods Appl. Sci., 28(13): 2557–2597, 2018. [arxiv]
  31. V. Nikolić and B. Kaltenbacher: Sensitivity analysis for shape optimization of a focusing acoustic lens in lithotripsy, Appl. Math. Opt., 76(2): 261–301, 2017. [arxiv]
  32. V. Nikolić and B. Kaltenbacher: On higher regularity for the Westervelt equation with strong nonlinear damping, Appl. Anal., 95(12): 2824–2840, 2016. [arxiv]
  33. V. Nikolić: Local existence results for the Westervelt equation with nonlinear damping and Neumann as well as absorbing boundary conditions, J. Math. Anal. Appl., 427(2): 1131–1175, 2015. [arxiv]
  34. B. Kaltenbacher, V. Nikolić, and M. Thalhammer: Efficient time integration methods based on operator splitting and application to the Westervelt equation, IMA J. Numer. Anal., 35(3): 1092–1124, 2015. [arxiv]
 
Edited volumes