Finite element discretization of nonlinear models of ultrasound heating

Authors: Careaga, Julio, Dörich, Benjamin, Nikolić, Vanja

Subject Terms: Mathematics - Numerical Analysis, 35L05, 35L72, 34A34

Access URL: http://arxiv.org/abs/2501.18307

Combined DG-CG finite element method for the Westervelt equation

Authors: Gómez, Sergio, Nikolić, Vanja

Subject Terms: Mathematics - Numerical Analysis, Mathematics - Analysis of PDEs, 65M50, 65M60, 35L70

Access URL: http://arxiv.org/abs/2412.09095

Westervelt-based modeling of ultrasound-enhanced drug delivery

Authors: Careaga, Julio, Nikolić, Vanja, Said-Houari, Belkacem

Subject Terms: Mathematics - Analysis of PDEs

Access URL: http://arxiv.org/abs/2412.07490

Mathematical models for nonlinear ultrasound contrast imaging with microbubbles

Authors: Nikolić, Vanja, Rauscher, Teresa

Subject Terms: Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis, 35L05, 35L72, 34A34

Access URL: http://arxiv.org/abs/2408.06108

Application of the thin-film equations in modelling of Marangoni flow patterns amongst surfactant source and drain locations

Authors: Careaga, Julio, Korevaar, Peter A., Nikolić, Vanja, Scarabosio, Laura

Subject Terms: Physics - Fluid Dynamics, Nonlinear Sciences - Adaptation and Self-Organizing Systems, 65N06, 76T20, 76B45, G.1.8, G.1.10

Access URL: http://arxiv.org/abs/2407.11868

Existence of solutions to k-Wave models of nonlinear ultrasound propagation in biological tissue

Authors: Cox, Ben, Kaltenbacher, Barbara, Nikolić, Vanja, Lucka, Felix

Subject Terms: Mathematics - Analysis of PDEs

Access URL: http://arxiv.org/abs/2405.20894

$L^\infty$ blow-up in the Jordan-Moore-Gibson-Thompson equation

Authors: Nikolić, Vanja, Winkler, Michael

Subject Terms: Mathematics - Analysis of PDEs

Access URL: http://arxiv.org/abs/2402.01595

Robust fully discrete error bounds for the Kuznetsov equation in the inviscid limit

Authors: Dörich, Benjamin, Nikolić, Vanja

Subject Terms: Mathematics - Numerical Analysis, 65M12, 65M15, 35L72, 65M60

Access URL: http://arxiv.org/abs/2401.06492

Homotopy trust-region method for phase-field approximations in perimeter-regularized binary optimal control

Authors: Manns, Paul, Nikolić, Vanja

Subject Terms: Mathematics - Optimization and Control, 49M05, 49M20, 49Q15

Access URL: http://arxiv.org/abs/2310.12478

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Asymptotic-preserving finite element analysis of Westervelt-type wave equations

Authors: Nikolić, Vanja

Subject Terms: Mathematics - Numerical Analysis, 35L72, 65M60

Access URL: http://arxiv.org/abs/2303.10743

The vanishing relaxation time behavior of multi-term nonlocal Jordan-Moore-Gibson-Thompson equations

Authors: Kaltenbacher, Barbara, Nikolić, Vanja

Subject Terms: Mathematics - Analysis of PDEs, 35L75, 35B25

Access URL: http://arxiv.org/abs/2302.06196

Nonlinear acoustic equations of fractional higher order at the singular limit

Authors: Nikolić, Vanja

Subject Terms: Mathematics - Analysis of PDEs, 35L75, 35B25

Access URL: http://arxiv.org/abs/2302.05112

Time-weighted estimates for the Blackstock equation in nonlinear ultrasonics

Authors: Nikolić, Vanja, Said-Houari, Belkacem

Subject Terms: Mathematics - Analysis of PDEs, 35A01, 35L05

Access URL: http://arxiv.org/abs/2210.08341

Mixed approximation of nonlinear acoustic equations: Well-posedness and a priori error analysis

Authors: Meliani, Mostafa, Nikolić, Vanja

Subject Terms: Mathematics - Numerical Analysis, Mathematics - Analysis of PDEs, 35L05, 35L72, 65M12, 65M15, 65M60

Access URL: http://arxiv.org/abs/2209.02737

Limiting behavior of quasilinear wave equations with fractional-type dissipation

Authors: Kaltenbacher Barbara, Meliani Mostafa, Nikolić Vanja

Source: Advanced Nonlinear Studies, Vol 24, Iss 3, Pp 748-774 (2024)

Subject Terms: quasilinear wave equations, westervelt’s equation, fractional dissipation, well-posedness, singular limits, 35l05, 35l72, 35r11, Mathematics, QA1-939

File Description: electronic resource

Relation: https://doaj.org/toc/2169-0375

Access URL: https://doaj.org/article/8555c86ff81a4ab28768b79314faa7bd

Limiting behavior of quasilinear wave equations with fractional-type dissipation

Authors: Kaltenbacher, Barbara, Meliani, Mostafa, Nikolić, Vanja

Subject Terms: Mathematics - Analysis of PDEs, 35L05, 35L72

Access URL: http://arxiv.org/abs/2206.15245

[formula omitted] blow-up in the Jordan–Moore–Gibson–Thompson equation

Authors: Nikolić, Vanja ^{a, ⁎}, Winkler, Michael ^b

Source: In Nonlinear Analysis October 2024 247

Determining kernels in linear viscoelasticity

Authors: Kaltenbacher, Barbara, Khristenko, Ustim, Nikolić, Vanja, Rajendran, Mabel Lizzy, Wohlmuth, Barbara

Subject Terms: Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis, Mathematics - Optimization and Control, 74B99, 35R30, 65J20

Access URL: http://arxiv.org/abs/2112.14071

A phase-field approach to shape and topology optimization of acoustic waves in dissipative media

Authors: Garcke, Harald, Mitra, Sourav, Nikolić, Vanja

Subject Terms: Mathematics - Optimization and Control, Mathematical Physics, Mathematics - Analysis of PDEs, 35L72, 49J20

Access URL: http://arxiv.org/abs/2109.13239