Výsledky vyhledávání - "Smoothness and regularity of solutions to PDEs"

Implicit integration factor method coupled with Padé approximation strategy for nonlocal Allen-Cahn equation

Autoři: Yuxin Zhang Hengfei Ding

Zdroj: Applied Numerical Mathematics. 213:88-107

Témata: energy stability, implicit integration factor method, Smoothness and regularity of solutions to PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, discrete maximum principle, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Riesz derivative

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2502.02089
https://zbmath.org/8034919
https://doi.org/10.1016/j.apnum.2025.02.019

Analytic smoothing effect for the non-cutoff Vlasov-Poisson-Boltzmann system with hard potentials

Autoři: Lvqiao Liu Hao Wang

Zdroj: Journal of Differential Equations. 427:442-477

Témata: non-cutoff, Boltzmann equations, Vlasov-Poisson-Boltzmann system, Smoothness and regularity of solutions to PDEs, Perturbations in context of PDEs, analytic smoothing effect, Vlasov equations

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/8017126
https://doi.org/10.1016/j.jde.2025.01.087

Uniqueness and Root-Lipschitz Regularity for a Degenerate Heat Equation: Uniqueness and root-Lipschitz regularity for a degenerate heat equation

Autoři: Alexander Dunlap Cole Graham

Zdroj: SIAM Journal on Mathematical Analysis. 57:1866-1891

Témata: Quasilinear parabolic equations, regularity, Smoothness and regularity of solutions to PDEs, Probability (math.PR), uniqueness, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, Strong solutions to PDEs, Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs, Degenerate parabolic equations, Stochastic ordinary differential equations (aspects of stochastic analysis), Blow-up in context of PDEs, Mathematics - Analysis of PDEs, degenerate parabolic equation, FOS: Mathematics, 35B65 (Primary), 35B53, 35K59, 35B44, 60H10 (Secondary), blow-up, Mathematics - Probability, Analysis of PDEs (math.AP)

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2308.11820

Epsilon-regularity for the Brakke flow with boundary

Autoři: Gasparetto, Carlo

Zdroj: Analysis & PDE. 18:857-894

Témata: Mathematics - Differential Geometry, Brakke flows, \(\varepsilon\)-regularity, Smoothness and regularity of solutions to PDEs, Flows related to mean curvature, 01 natural sciences, small perturbation solutions, Viscosity solutions to PDEs, 53E10 (Primary) 35D40, 35B65 (Secondary), varifolds, boundary regularity, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Brakke's theorem, viscosity, FOS: Mathematics, mean curvature flows, Allard's theorem, 0101 mathematics, Analysis of PDEs (math.AP)

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2206.08830
https://zbmath.org/8023888
https://doi.org/10.2140/apde.2025.18.857

Maxwell’s equations with hypersingularities at a negative index material conical tip: Maxwell's equations with hypersingularities at a negative index material conical tip

Autoři: Bonnet-Ben, Anne-Sophie Chesnel, Lucas Rihani, Mahran a další

Přispěvatelé: Bonnet-Ben, Anne-Sophie Chesnel, Lucas Rihani, Mahran a další

Zdroj: Pure and Applied Analysis. 7:127-169

Témata: Variational methods applied to problems in optics and electromagnetic theory, black hole singularities, 35B65, Smoothness and regularity of solutions to PDEs, Composite media, random media in optics and electromagnetic theory, limiting radiation principle, [MATH] Mathematics [math], 78M30, Mathematics - Analysis of PDEs, Maxwell equations, Maxwell's equations, 78A48, Electromagnetic theory (general), Mandelstam radiation principle, 35Q61, FOS: Mathematics, negative index materials, [MATH]Mathematics [math], MSC: 78A25, Kondratiev theory, Analysis of PDEs (math.AP)

Popis souboru: application/xml; application/pdf

Přístupová URL adresa: http://arxiv.org/abs/2305.01982
https://zbmath.org/8014453
https://doi.org/10.2140/paa.2025.7.127
https://hal.science/hal-04087360v2

Caffarelli’s work on elliptic free boundary problems: Caffarelli's work on elliptic free boundary problems

Autoři: De Lellis, Camillo

Zdroj: Bulletin of the American Mathematical Society. 62:273-300

Témata: Mathematics - Analysis of PDEs, regularity theory for elliptic free boundary problems, Smoothness and regularity of solutions to PDEs, Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators, FOS: Mathematics, History of partial differential equations, Free boundary problems for PDEs, Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators, 35R35, 35J15, 35J20, Biographies, obituaries, personalia, bibliographies, Analysis of PDEs (math.AP)

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2408.07007

Numerical Approximation of Discontinuous Solutions of the Semilinear Wave Equation: Numerical approximation of discontinuous solutions of the semilinear wave equation

Autoři: Jiachuan Cao Buyang Li Yanping Lin a další

Zdroj: SIAM Journal on Numerical Analysis. 63:214-238

Témata: Smoothness and regularity of solutions to PDEs, high-/low-frequency decomposition, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Numerical Analysis (math.NA), Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), Error bounds for initial value and initial-boundary value problems involving PDEs, KdV equations (Korteweg-de Vries equations), error estimates, Numerical interpolation, semilinear wave equation, discontinuous solution, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, low regularity, Numerical methods for discrete and fast Fourier transforms, numerical approximation

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2312.10392
https://zbmath.org/7981229
https://doi.org/10.1137/24m1635879

Numerical approximation for stochastic nonlinear fractional diffusion equation driven by rough noise

Autoři: Daxin Nie Jing Sun Weihua Deng

Zdroj: ESAIM: Mathematical Modelling and Numerical Analysis. 59:389-418

Témata: Numerical solutions to stochastic differential and integral equations, Smoothness and regularity of solutions to PDEs, finite element method, Fractional processes, including fractional Brownian motion, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, fractional Brownian sheet, Numerical quadrature and cubature formulas, Fractional partial differential equations, 01 natural sciences, Wong-Zakai approximation, Error bounds for initial value and initial-boundary value problems involving PDEs, stochastic fractional diffusion equation, Fractional derivatives and integrals, convolution quadrature, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, PDEs with randomness, stochastic partial differential equations, Mathematics - Numerical Analysis, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, error analysis

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2201.10897

Łojasiewicz inequalities, uniqueness and rigidity for cylindrical self-shrinkers: Łojasiewic inequalities, uniqueness and rigidity for cylindrical self-shrinkers

Autoři: Zhu, Jonathan J.

Zdroj: Cambridge Journal of Mathematics. 13:173-224

Témata: Mathematics - Differential Geometry, Blow-up in context of PDEs, mean curvature flow, Differential Geometry (math.DG), 53E10, 53C42, Smoothness and regularity of solutions to PDEs, Flows related to mean curvature, FOS: Mathematics, Abresch-Langer curves, Łojasiewicz inequalities, A priori estimates in context of PDEs

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2011.01633

Serrin-type blowup Criterion for the degenerate compressible Navier-Stokes equations: Serrin-type blowup criterion for the degenerate compressible Navier-Stokes equations

Autoři: Zhigang Wang

Zdroj: Communications in Analysis and Mechanics, Vol 17, Iss 1, Pp 145-158 (2025)

Témata: Compressible Navier-Stokes equations, degenerate viscosity, Classical solutions to PDEs, Smoothness and regularity of solutions to PDEs, QA801-939, Analytic mechanics, Gas dynamics (general theory), Existence problems for PDEs: global existence, local existence, non-existence, compressible navier–stokes equations, Blow-up in context of PDEs, classical solutions, far-field vacuum, compressible Navier-Stokes equations, Navier-Stokes equations, serrin-type blowup criterion, Serrin-type blow-up criterion

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/8015295
https://doi.org/10.3934/cam.2025007
https://doaj.org/article/03e2237de0df4eb880bbadd4fd737f5b

Fractional-order dependent Radial basis functions meshless methods for the integral fractional Laplacian: Fractional-order dependent radial basis functions meshless methods for the integral fractional Laplacian

Autoři: Zhaopeng Hao Zhiqiang Cai Zhongqiang Zhang

Zdroj: Computers & Mathematics with Applications. 178:197-213

Témata: pseudo-spectral collocation methods, Fractional derivatives and integrals, Smoothness and regularity of solutions to PDEs, FOS: Mathematics, Rate of convergence, degree of approximation, radial basis functions, meshless method, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), integral fractional Laplacian, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2411.10675

Modified Wasserstein gradient flow formulation of time-fractional porous medium equations with nonlocal pressure

Autoři: Nhan-Phu Chung Thanh-Son Trinh

Zdroj: Discrete and Continuous Dynamical Systems - B. 30:3601-3624

Témata: modified Wasserstein distance, gradient flow, Quasilinear parabolic equations, Mathematics - Analysis of PDEs, Smoothness and regularity of solutions to PDEs, FOS: Mathematics, JKO scheme, time-fractional porous medium equation, fractional Laplacian, Degenerate parabolic equations, Fractional partial differential equations, Analysis of PDEs (math.AP)

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2409.08441

Boundary Riesz potential estimates for parabolic equations with measurable nonlinearities

Autoři: Lee, Ho-Sik Kim, Youchan

Zdroj: Communications in Analysis and Mechanics, Vol 17, Iss 1, Pp 61-99 (2025)

Témata: riesz potentials, measurable nonlinearities, PDEs with low regular coefficients and/or low regular data, Riesz potentials, Smoothness and regularity of solutions to PDEs, Initial-boundary value problems for second-order parabolic equations, QA801-939, nonlinear parabolic equations, Analytic mechanics, Nonlinear parabolic equations, PDEs with measure, A priori estimates in context of PDEs, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Popis souboru: application/xml

Přístupová URL adresa: https://doaj.org/article/753a5937591c43ea822c8d162ecba479

A sharp Li-Yau gradient bound on compact manifolds

Autoři: Zhang, Qi S.

Zdroj: Communications in Analysis and Geometry. 33:261-274

Témata: Mathematics - Differential Geometry, Riemannian manifolds, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Smoothness and regularity of solutions to PDEs, Heat equation, Li-Yau estimates, FOS: Mathematics, Methods of global Riemannian geometry, including PDE methods, curvature restrictions, 0101 mathematics, 01 natural sciences, 53C44, Analysis of PDEs (math.AP)

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2110.08933

The ADMM-PINNs Algorithmic Framework for Nonsmooth PDE-Constrained Optimization: A Deep Learning Approach: The ADMM-PINNs algorithmic framework for nonsmooth PDE-constrained optimization: a deep learning approach

Autoři: Yongcun Song Xiaoming Yuan Hangrui Yue

Zdroj: SIAM Journal on Scientific Computing. 46:C659-C687

Témata: PDEs in connection with control and optimization, FOS: Computer and information sciences, Numerical optimization and variational techniques, Inverse problems for PDEs, Computer Science - Machine Learning, Control/observation systems governed by partial differential equations, Numerical methods based on nonlinear programming, Smoothness and regularity of solutions to PDEs, Nonsmooth analysis, deep learning, PDE constrained optimization (numerical aspects), 01 natural sciences, nonsmooth optimization, Machine Learning (cs.LG), physics-informed neural networks, Optimization and Control (math.OC), FOS: Mathematics, PDE-constrained optimization, 0101 mathematics, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, ADMM, Mathematics - Optimization and Control, Artificial neural networks and deep learning

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2302.08309
https://zbmath.org/7955192
https://doi.org/10.1137/23m1566935

Complex analytic solutions for the TQG model

Autoři: Prince Romeo Mensah

Zdroj: Analysis. 45:129-138

Témata: thermal quasi-geostrophic, Gevrey class, Mathematics - Complex Variables, Smoothness and regularity of solutions to PDEs, analyticity, 01 natural sciences, Mathematics - Analysis of PDEs, Dynamical systems in fluid mechanics, oceanography and meteorology, holomorphic function, 0103 physical sciences, Existence, uniqueness, and regularity theory for incompressible inviscid fluids, FOS: Mathematics, oceanography, Complex Variables (math.CV), 0101 mathematics, Analysis of PDEs (math.AP)

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2405.00575

The modelling error in multi-dimensional time-dependent solute transport models

Autoři: Masri, Rami Zeinhofer, Marius Kuchta, Miroslav a další

Zdroj: arXiv

Témata: Physiological flow, 0301 basic medicine, Smoothness and regularity of solutions to PDEs, Flows in porous media, filtration, seepage, Numerical Analysis (math.NA), PDEs in connection with fluid mechanics, Physiological flows, A priori estimates in context of PDEs, modeling error in evolving Bochner spaces, Diffusion, solute transport models, Second-order elliptic equations, 03 medical and health sciences, Error bounds for initial value and initial-boundary value problems involving PDEs, Mathematics - Analysis of PDEs, 0302 clinical medicine, 35K45, 65G99, 65J08, 65M15, 92-10, FOS: Mathematics, time dependent convection-diffusion, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, multi-dimensional modeling, Mathematics - Numerical Analysis, Computational methods for problems pertaining to biology, Finite element methods applied to problems in fluid mechanics, Analysis of PDEs (math.AP)

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2303.17999
https://zbmath.org/7957223
https://doi.org/10.1051/m2an/2024060

Effect of random noises on pathwise solutions to the high-dimensional modified Euler-Poincaré system

Autoři: Zhang, Lei

Zdroj: Journal of Differential Equations. 403:87-157

Témata: Water waves, gravity waves, dispersion and scattering, nonlinear interaction, Applications of Lie (super)algebras to physics, etc, high-dimensional modified Euler-Poincaré system, Perturbations in context of PDEs, Smoothness and regularity of solutions to PDEs, Probability (math.PR), Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, Strong solutions to PDEs, blow-up criteria, Euler equations, stochastic perturbation, Blow-up in context of PDEs, Mathematics - Analysis of PDEs, Stochastic partial differential equations (aspects of stochastic analysis), FOS: Mathematics, local and global solutions, PDEs with randomness, stochastic partial differential equations, Mathematics - Probability, Analysis of PDEs (math.AP)

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2107.09603

A singular Dirichlet problem for the Monge-Ampère type equation

Autoři: Zhang, Zhijun Zhang, Bo

Zdroj: Acta Mathematica Scientia. 44:1965-1983

Témata: Monge-Ampère equations, global asymptotic behavior, Smoothness and regularity of solutions to PDEs, Affine differential geometry, singular boundary value problem, Monge-Ampère equation, unique convex solution, Nonlinear elliptic equations

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/7906355
https://doi.org/10.1007/s10473-024-0520-5

Almost periodic solutions of the parabolic-elliptic Keller–Segel system on the whole space: Almost periodic solutions of the parabolic-elliptic Keller-Segel system on the whole space

Autoři: Nguyen Thi Loan Pham Truong Xuan

Zdroj: Archiv der Mathematik. 123:431-446

Témata: Almost and pseudo-almost periodic solutions to PDEs, Quasilinear parabolic equations, Lorentz spaces, Smoothness and regularity of solutions to PDEs, Cell movement (chemotaxis, etc.), dispersive (smoothing) estimates, Keller-Segel system, almost periodic solutions, polynomial stability

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/7930067
https://doi.org/10.1007/s00013-024-02023-8