Energy Stable and Maximum Bound Principle Preserving Schemes for the \(\boldsymbol {Q}\)-Tensor Flow of Liquid Crystals: Energy stable and maximum bound principle preserving schemes for the \(Q\)-tensor flow of liquid crystals

Συγγραφείς: Dianming Hou, Xiaoli Li, Zhonghua Qiao, Nan Zheng

Πηγή: SIAM Journal on Numerical Analysis. 63:854-880

Θεματικοί όροι: energy stability, Error bounds for initial value and initial-boundary value problems involving PDEs, error estimates, \(Q\)-tensor, FOS: Mathematics, Initial-boundary value problems for higher-order parabolic equations, liquid crystal, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, maximum bound principle

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2309.02657

An inverse problem of determining the parameters in diffusion equations by using fractional physics-informed neural networks

Συγγραφείς: M. Srati, A. Oulmelk, L. Afraites, A. Hadri, M.A. Zaky, A. Aldraiweesh, A.S. Hendy

Πηγή: Applied Numerical Mathematics. 208:189-213

Θεματικοί όροι: time-fractional diffusion equations, Numerical optimization and variational techniques, Inverse problems for PDEs, Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs, Nonconvex programming, global optimization, Fractional partial differential equations, alternating direction multiplier method, inverse parameter problem, Fractional derivatives and integrals, physics-informed neural network method, Initial-boundary value problems for higher-order parabolic equations, DeepONets method, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, gradient descent method, Artificial neural networks and deep learning

Περιγραφή αρχείου: application/xml

Second-Order Linear Stabilized Semi-Implicit Crank-Nicolson Scheme for the Cahn-Hilliard Model with Dynamic Boundary Conditions: Second-order linear stabilized semi-implicit Crank-Nicolson scheme for the Cahn-Hilliard model with dynamic boundary conditions

Συγγραφείς: Meng, Xiangjun, Bao, Xuelian, Zhang, Zhengru

Πηγή: Communications in Computational Physics. 37:137-170

Θεματικοί όροι: second-order Crank-Nicolson formula, energy stability, reaction rate, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Initial-boundary value problems for higher-order parabolic equations, PDEs in connection with fluid mechanics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, dynamic boundary conditions, Cahn-Hilliard equation, convergence analysis

Περιγραφή αρχείου: application/xml

A nonnegative weak solution to the phase field crystal model with degenerate mobility

Συγγραφείς: Luong, Toai, Wise, Steven M.

Πηγή: Discrete and Continuous Dynamical Systems - B. 30:3288-3309

Θεματικοί όροι: positive solution, phase field crystal, energy inequality, weak solution, Initial-boundary value problems for higher-order parabolic equations, Weak solutions to PDEs, Degenerate parabolic equations, degenerate mobility

Περιγραφή αρχείου: application/xml

Improved Scalar Auxiliary Variable Schemes for Original Energy Stability of Gradient Flows: Improved scalar auxiliary variable schemes for original energy stability of gradient flows

Συγγραφείς: Rui Chen, Tingfeng Wang, Xiaofei Zhao

Πηγή: Journal of Scientific Computing. 103

Θεματικοί όροι: convergence, Applications to the sciences, Initial-boundary value problems for second-order parabolic equations, gradient flows, Allen-Cahn and Cahn-Hilliard equations, improved scalar auxiliary variable scheme, FOS: Mathematics, Nonlinear parabolic equations, Initial-boundary value problems for higher-order parabolic equations, original energy stability, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2405.03403
https://zbmath.org/8018369
https://doi.org/10.1007/s10915-025-02796-2

Second-Order, Energy-Stable and Maximum Bound Principle Preserving Schemes for Two-Phase Incompressible Flow: Second-order, energy-stable and maximum bound principle preserving schemes for two-phase incompressible flow

Συγγραφείς: Xiaoli Li, Hao Liu, Nan Zheng

Συνεισφορές: Department of Applied Mathematics

Πηγή: Journal of Scientific Computing. 102

Θεματικοί όροι: energy dissipation, Navier–Stokes, Energy dissipation, Navier-Stokes, second-order, Maximum bound principle, Error bounds for initial value and initial-boundary value problems involving PDEs, Allen-Cahn, MAC scheme, Second-order, Initial-boundary value problems for higher-order parabolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, maximum bound principle

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N‐fold Darboux transformation of the discrete PT‐symmetric nonlinear Schrödinger equation and new soliton solutions over the nonzero background: \(N\)-fold Darboux transformation of the discrete PT-symmetric nonlinear Schrödinger equation and new soliton solutions over the nonzero background

Συγγραφείς: Xu, Tao, An, Li-Cong, Li, Min, Xu, Chuan-Xin

Πηγή: Studies in Applied Mathematics. 152:1338-1364

Θεματικοί όροι: NLS equations (nonlinear Schrödinger equations), Asymptotic behavior of solutions to PDEs, Second-order parabolic systems, 01 natural sciences, discrete PT-symmetric nonlinear Schrödinger equation, asymptotic analysis, soliton solutions, Soliton solutions, Time-dependent Schrödinger equations and Dirac equations, 0103 physical sciences, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Initial-boundary value problems for higher-order parabolic equations, 0101 mathematics, Darboux transformation

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A BDF2-SSAV Numerical Scheme with Fourier-Spectral Method for a Droplet Thin Film Coarsening Model: A BDF2-SSAV numerical scheme with Fourier-spectral method for a droplet thin film coarsening model

Συγγραφείς: Zhang, Juan, Dong, Lixiu, Zhang, Zhengru

Πηγή: Numerical Mathematics: Theory, Methods and Applications. 17:777-804

Θεματικοί όροι: energy stability, droplet coarsening model, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Fourier-spectral method, Nonlinear parabolic equations, Initial-boundary value problems for higher-order parabolic equations, Variational inequalities, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, optimal rate convergence analysis, scalar auxiliary variable

Περιγραφή αρχείου: application/xml

Global dynamical behavior of solutions for finite degenerate fourth-order parabolic equations with mean curvature nonlinearity

Συγγραφείς: Yuxuan Chen

Πηγή: Communications in Analysis and Mechanics, Vol 15, Iss 4, Pp 658-694 (2023)

Θεματικοί όροι: global existence, finite time blow up, Blow-up in context of PDEs, Quasilinear parabolic equations, ground state solution, degenerate parabolic equation, Asymptotic behavior of solutions to PDEs, QA801-939, Analytic mechanics, Initial-boundary value problems for higher-order parabolic equations, Weak solutions to PDEs, Degenerate parabolic equations, finite-time blow-up

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/7919371
https://doi.org/10.3934/cam.2023033
https://doaj.org/article/65e15d17d2ac44b9b9a90c19ef45f16f

Well-posedness and dynamic properties of solutions to a class of fourth order parabolic equation with mean curvature nonlinearity

Συγγραφείς: Zhang, Xin, Zhou, Jun

Πηγή: Discrete and Continuous Dynamical Systems - B. 28:3768-3806

Θεματικοί όροι: global existence, Blow-up in context of PDEs, Quasilinear parabolic equations, Attractors, Quasilinear parabolic equations with mean curvature operator, Initial-boundary value problems for higher-order parabolic equations, mean curvature nonlinearity, Thin fluid films, blow-up, fourth order parabolic equations

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/7675830
https://doi.org/10.3934/dcdsb.2022240

Improving the accuracy and consistency of the energy quadratization method with an energy-optimized technique

Συγγραφείς: Xiaoqing Meng, Aijie Cheng, Zhengguang Liu

Πηγή: Journal of Computational and Applied Mathematics. 459:116368

Θεματικοί όροι: unconditional energy stability, invariant energy quadratization, Numerical Analysis (math.NA), gradient flow models, energy-optimized technique, Initial-boundary value problems for second-order parabolic equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Nonlinear parabolic equations, Initial-boundary value problems for higher-order parabolic equations, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, numerical experiments, 65M12, 35K20, 35K35, 35K55, 65Z05

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2404.01747
https://zbmath.org/7968679
https://doi.org/10.1016/j.cam.2024.116368

General numerical framework to derive structure preserving reduced order models for thermodynamically consistent reversible-irreversible PDEs

Συγγραφείς: Zengyan Zhang, Jia Zhao

Πηγή: Journal of Computational Physics. 521:113562

Θεματικοί όροι: phase field, thermodynamically consistent, model order reduction, structure preserving, FOS: Mathematics, Initial-boundary value problems for higher-order parabolic equations, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 0101 mathematics, 7. Clean energy, 01 natural sciences, Chemical kinetics in thermodynamics and heat transfer

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2312.02363
https://zbmath.org/7974297
https://doi.org/10.1016/j.jcp.2024.113562

Global existence and blow-up of weak solutions for a fourth-order parabolic equation with gradient nonlinearity

Συγγραφείς: Zhao, Jinhong, Guo, Bin, Wang, Jian

Πηγή: Zeitschrift für angewandte Mathematik und Physik. 75

Θεματικοί όροι: fourth-order parabolic equation, global existence, Blow-up in context of PDEs, Initial-boundary value problems for higher-order parabolic equations, gradient nonlinearity, Semilinear parabolic equations, blow-up

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/7812527
https://doi.org/10.1007/s00033-023-02148-w

Local solvability of fully nonlinear parabolic problems of higher order

Συγγραφείς: Romanenko, I.B.

Θεματικοί όροι: Degree theory for nonlinear operators, \((S_+)\) conditions, Nonlinear parabolic equations, uniqueness, Initial-boundary value problems for higher-order parabolic equations, topological methods, Local existence and uniqueness theorems (PDE)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2027883
http://dspace.nbuv.gov.ua/handle/123456789/169252

One-dimensional flow of a compressible viscous micropolar fluid: The Cauchy problem: One-dimensional flow of a compressible viscous micropolar fluid: the Cauchy problem

Συγγραφείς: Mujaković, N.

Πηγή: Mathematical Communications
Volume 10
Issue 1

Θεματικοί όροι: Cauchy problem, existence, uniqueness, PDEs in connection with fluid mechanics, Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics, micropolar fluid, the Cauchy problem, compressible fluid, thermodynamics, evolution problem, strong solution, weak convergence, Initial-boundary value problems for higher-order parabolic equations, viscous fluid

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: https://www.bib.irb.hr/376336
https://zbmath.org/2203976
http://atlas-conferences.com/c/a/m/r/43.htm
https://hrcak.srce.hr/file/1329
https://hrcak.srce.hr/655
https://hrcak.srce.hr/655

Subcritical Kuramoto–Sivashinsky-type equation on a half-line: Subcritical Kuramoto-Sivashinsky-type equation on a half-line

Συγγραφείς: Elena I. Kaikina

Πηγή: Journal of Differential Equations. 220:279-321

Θεματικοί όροι: Initial-boundary value problem, Kuramoto–Sivashinsky equation, Large-time asymptotics, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Asymptotic behavior of solutions to PDEs, large-time asymptotics, Initial-boundary value problems for higher-order parabolic equations, 0101 mathematics, initial-boundary value problem, 01 natural sciences, Analysis

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2242188
https://doi.org/10.1016/j.jde.2005.03.002
https://www.sciencedirect.com/science/article/pii/S0022039605000847
https://ui.adsabs.harvard.edu/abs/2006JDE...220..279K/abstract
https://core.ac.uk/display/82465518

Existence and Positivity of Solutions of a Fourth-Order Nonlinear PDE Describing Interface Fluctuations: Existence and positivity of solutions of a fourth-order nonlinear PDE describing interface fluctuations

Συγγραφείς: Eugene R. Speer, Pavel Bleher, Joel L. Lebowitz

Πηγή: From the Microscopic to the Macroscopic ISBN: 9789819819553

Θεματικοί όροι: interface fluctuations, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Asymptotic behavior of solutions to PDEs, families of Lyapunov functions, positivity preservation, Initial value problems for linear higher-order PDEs, Initial-boundary value problems for higher-order parabolic equations, 0101 mathematics, 01 natural sciences, Higher-order parabolic equations

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/687748
https://doi.org/10.1002/cpa.3160470702
https://www.science.iupui.edu/~bleher/Papers/1994_Existence_and_Positivity.pdf
https://www.researchwithrutgers.com/en/publications/existence-and-positivity-of-solutions-of-a-fourthorder-nonlinear-
http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160470702/abstract

Stabilization of a solution of the first mixed problem for a quasi-elliptic evolution equation

Συγγραφείς: L. M. Kozhevnikova

Πηγή: Sbornik: Mathematics. 196:999-1032

Θεματικοί όροι: homogeneous boundary conditions, Asymptotic behavior of solutions to PDEs, higher-order equation, Quasielliptic equations, Initial-boundary value problems for higher-order parabolic equations, 0101 mathematics, compactly supported initial function, unbounded domains, Stability in context of PDEs, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://ui.adsabs.harvard.edu/abs/2005SbMat.196..999K/abstract
https://www.physicsweb.org/article/10.1070/SM2005v196n07ABEH000946
http://iopscience.iop.org/article/10.1070/SM2005v196n07ABEH000946

Bifurcating periodic solutions of wind-driven circulation equations

Συγγραφείς: W.G. Price, Zhi-Min Chen

Πηγή: Journal of Mathematical Analysis and Applications. 304:783-796

Θεματικοί όροι: Bifurcations in context of PDEs, Navier–Stokes equation, Hydrology, hydrography, oceanography, Applied Mathematics, Navier-Stokes equations for incompressible viscous fluids, 01 natural sciences, Navier-Stokes equation, Periodic solution, Nonlinear parabolic equations, Initial-boundary value problems for higher-order parabolic equations, Hopf bifurcation, 0101 mathematics, Bessel-potential space, Analysis, Periodic solutions to PDEs, 0105 earth and related environmental sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2157716
https://doi.org/10.1016/j.jmaa.2004.09.062
https://core.ac.uk/display/82639838
https://www.sciencedirect.com/science/article/pii/S0022247X04008170
https://ui.adsabs.harvard.edu/abs/2005JMAA..304..783C/abstract
https://eprints.soton.ac.uk/23648/

On a Cahn–Hilliard model for phase separation with elastic misfit: On a Cahn--Hilliard model for phase separation with elastic misfit

Συγγραφείς: Garcke, Harald

Πηγή: Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 22:165-185

Θεματικοί όροι: ddc:510, logarithmic singularity, Smoothness and regularity of solutions to PDEs, 510 Mathematik, Dynamic and nonequilibrium phase transitions (general) in statistical mechanics, A priori estimates in context of PDEs, 01 natural sciences, elliptic-parabolic systems, Nonlinear parabolic equations, Initial-boundary value problems for higher-order parabolic equations, 0101 mathematics, \(L^p\)-estimates for gradients, Mathematical Physics, Analysis

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: https://ems.press/content/serial-article-files/16517
https://zbmath.org/2165097
https://doi.org/10.1016/j.anihpc.2004.07.001
https://epub.uni-regensburg.de/10964/
https://eudml.org/doc/78652
https://www.sciencedirect.com/science/article/abs/pii/S0294144904000642
https://www.sciencedirect.com/science/article/pii/S0294144904000642#!
https://www.sciencedirect.com/science/article/pii/S0294144904000642
http://ui.adsabs.harvard.edu/abs/2005AIHPC..22..165G/abstract
https://epub.uni-regensburg.de/10964/