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

Near-Boundary Asymptotics and Unique Continuation for the AdS--Einstein--Maxwell System

Authors: Guisset, Simon

Subject Terms: General Relativity and Quantum Cosmology, High Energy Physics - Theory, Mathematics - Analysis of PDEs, 83C05. 35A02 (primary), 83E05, 35L72 (secondary)

Access URL: http://arxiv.org/abs/2501.10298

The Modified Energy Method for Quasilinear Wave Equations of Kirchhoff Type

Authors: Martinez, Ryan

Subject Terms: Mathematics - Analysis of PDEs, 35L72 (Primary) 37K45 (Secondary)

Access URL: http://arxiv.org/abs/2501.06384

Nonlinear interpolation and the flow map for quasilinear equations

Authors: Alazard, Thomas, Burq, Nicolas, Ifrim, Mihaela, Tataru, Daniel, Zuily, Claude

Subject Terms: Mathematics - Analysis of PDEs, 35L72, 35L77

Access URL: http://arxiv.org/abs/2410.06909

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

Blow-up of classical solutions of quasilinear wave equations in one space dimension

Authors: Haruyama, Yuki, Takamura, Hiroyuki

Source: Nonlinear Analysis, RWA, 81 (2025), Paper No.104212

Subject Terms: Mathematics - Analysis of PDEs, primary 35L72, secondary 35B44

Access URL: http://arxiv.org/abs/2404.06274

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

The Kuznetsov and Blackstock equations of nonlinear acoustics with nonlocal-in-time dissipation

Authors: Kaltenbacher, B., Meliani, M., Nikolić, V.

Subject Terms: Mathematics - Analysis of PDEs, 35L05, 35L72, 35R11

Access URL: http://arxiv.org/abs/2308.10580

Bulk-boundary correspondences and unique continuation in asymptotically Anti-de Sitter spacetimes

Authors: Shao, Arick

Subject Terms: General Relativity and Quantum Cosmology, High Energy Physics - Theory, Mathematics - Analysis of PDEs, Mathematics - Differential Geometry, 83C05. 35A02 (primary), 83E05, 35L72 (secondary)

Access URL: http://arxiv.org/abs/2307.09107

Asymptotic behavior of solutions to the Cauchy problem for 1-D p-system with space dependent damping

Authors: Matsumura, Akitaka, Nishihara, Kenji

Subject Terms: Mathematics - Analysis of PDEs, Mathematical Physics, 35L72(Primary), 76S05(Secondly)

Access URL: http://arxiv.org/abs/2307.05865

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

Almost global existence for Kirchhoff equations around global solutions

Authors: Ghisi, Marina, Gobbino, Massimo

Subject Terms: Mathematics - Analysis of PDEs, 35L90, 35L20, 35L72

Access URL: http://arxiv.org/abs/2302.09873

Supersonic flows of the Euler-Poisson system in three-dimensional cylinders

Authors: Bae, Myoungjean, Park, Hyangdong

Subject Terms: Mathematics - Analysis of PDEs, 35G60, 35J66, 35L72, 35M32, 76J20, 76N10

Access URL: http://arxiv.org/abs/2302.03308

Global existence and decay of small solutions for quasi-linear second-order uniformly dissipative hyperbolic-hyperbolic systems

Authors: Sroczinski, Matthias

Subject Terms: Mathematics - Analysis of PDEs, Primary 35A01, 35B35, 35L72, 35L15, 35S50, 35Q35, 35Q75

Access URL: http://arxiv.org/abs/2301.01685

A road map to the blow-up for a Kirchhoff equation with external force

Authors: Ghisi, Marina, Gobbino, Massimo

Subject Terms: Mathematics - Analysis of PDEs, Mathematics - Dynamical Systems, 35B44, 37J46, 35L90, 35L72

Access URL: http://arxiv.org/abs/2211.06711

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

Global solutions to the Kirchhoff equation with spectral gap data in the energy space

Authors: Ghisi, Marina, Gobbino, Massimo

Subject Terms: Mathematics - Analysis of PDEs, 35L90, 35L20, 35L72, 35D30

Access URL: http://arxiv.org/abs/2208.05400

The global solvability of the Kirchhoff equation with Sobolev data

Authors: Matsuyama, Tokio, Neyt, Lenny

Subject Terms: Mathematics - Analysis of PDEs, Mathematics - Functional Analysis, Primary 35L20, Secondary 35L72

Access URL: http://arxiv.org/abs/2207.02076

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