Preprints
 
 
Journal articles
 
  • M. Meliani and V. Nikolić: Analysis of general shape optimization problems in nonlinear acoustics, to appear in Appl Math Optim. [arxiv]

  • 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.

  • B. Kaltenbacher, U. Khristenko, V. Nikolić, M. L. Rajendran, and B. Wohlmuth: Determining kernels in linear viscoelasticity, J. Comput. Phys., 464, 2022. [arxiv]

  • H. Garcke, S. Mitra, and V. Nikolić: A phase-field approach to shape and topology optimization of acoustic waves in dissipative media, accepted in SIAM J. Control Optim., [arxiv]

  • B. Kaltenbacher and V. Nikolić: Time-fractional Moore–Gibson–Thompson equations, Math. Models Methods Appl. Sci., 32(5), 965–1013, 2022. [arxiv]
  • B. Kaltenbacher and V. Nikolić: Parabolic approximation of quasilinear wave equations with applications in nonlinear acoustics, SIAM J. Math. Anal., 54(2), 2022. [arxiv]

  • M. Muhr, V. Nikolić, and B. Wohlmuth: A discontinuous Galerkin coupling for nonlinear elasto-acoustics, to appear in IMA J. Numer. Anal., [arxiv]

  • 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., vol. 62, 2021. [arxiv]

  • 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]

  • V. Nikolić and B. Said-Houari: Mathematical analysis of memory effects and thermal relaxation in nonlinear sound waves on unbounded domains, J. Differ. Equat., vol. 273, 172-218, 2021. [arxiv]

  • 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(3), 2021. [arxiv]

  • 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., vol. 415, 2020. [arxiv]

  • 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]

  • 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]

  • 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]

  • 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]

  • 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]

  • 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]

  • 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]

  • 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]

  • V. Nikolić and B. Kaltenbacher: On higher regularity for the Westervelt equation with strong nonlinear damping, Appl. Anal., 95(12), 2824–2840, 2016. [arxiv]

  • 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]

  • 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]