Search Results - Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs*

Continuous dependence of thermoelasticity problem

Authors: Meyvaci, Müge Gür, Şevket

Source: Turkish Journal of Mathematics. 49:238-243

Subject Terms: Initial-boundary value problems for systems of linear higher-order PDEs, Thermal effects in solid mechanics, thermoelasticity, Perturbations in context of PDEs, Asymptotic behavior of solutions to PDEs, structural stability, continuous dependence, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Thermodynamics in solid mechanics

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Continuous dependence of a beam equation with products of two nonlinear components

Authors: Le Thi Phuong Ngoc Cao Quoc Duy Nguyen Huu Nhan et al.

Source: The Journal of Analysis. 33:839-864

Subject Terms: continuous dependence, Higher-order semilinear hyperbolic equations, beam equation, Faedo-Galerkin method, Rods (beams, columns, shafts, arches, rings, etc.), Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Initial-boundary value problems for higher-order hyperbolic equations

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Access URL: https://zbmath.org/8035926
https://doi.org/10.1007/s41478-024-00865-7

A remark on the vanishing diffusivity limit of the Keller-Segel equations in Besov spaces

Authors: Yu, Yanghai Liu, Fang

Source: Discrete and Continuous Dynamical Systems - B. 30:1607-1616

Subject Terms: Quasilinear parabolic equations, Mathematics - Analysis of PDEs, Initial value problems for second-order parabolic systems, inviscid limit, Cell movement (chemotaxis, etc.), Besov spaces, Existence, uniqueness, and regularity theory for incompressible inviscid fluids, FOS: Mathematics, Keller-Segel equations, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Singular perturbations in context of PDEs, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2310.10972

Cross-invariant sets of the coupled nonlinear Schrödinger system with harmonic potentials

Authors: Zhou, Xinlu Zhang, Jian

Source: Discrete and Continuous Dynamical Systems - B. 30:2729-2739

Subject Terms: global existence, Blow-up in context of PDEs, Variational methods applied to PDEs, NLS equations (nonlinear Schrödinger equations), Time-dependent Schrödinger equations and Dirac equations, coupled nonlinear Schrödinger system, Quantum dynamics and nonequilibrium statistical mechanics (general), Bose-Einstein condensates, Existence problems for PDEs: global existence, local existence, non-existence, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, sharp condition, cross-invariant sets

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Nonuniform dependence for high-dimensional modified Euler–Poincaré system with multiplicative noises: Nonuniform dependence for high-dimensional modified Euler-Poincaré system with multiplicative noises

Authors: Zhang, Lei Liu, Bin

Source: Stochastics and Dynamics. 25

Subject Terms: nonuniform dependence, stochastic MCH2 system, Stochastic partial differential equations (aspects of stochastic analysis), data-to-solution mapping, Applications of stochastic analysis (to PDEs, etc.), PDEs with randomness, stochastic partial differential equations, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs

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Access URL: https://zbmath.org/8037126
https://doi.org/10.1142/s021949372550011x

The Steady Relativistic Boltzmann Equation in Half-Space: The steady relativistic Boltzmann equation in half-space

Authors: Jing Ouyang Changguo Xiao

Source: Journal of Statistical Physics. 192

Subject Terms: Special relativity, Boltzmann equations, backward bi-characteristics, boundary layer problem, relativistic Boltzmann equation, Kinetic theory of gases in equilibrium statistical mechanics, PDEs in connection with relativity and gravitational theory, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, diffuse reflection boundary condition

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BOUNDARY LAYER-PRESERVING METHODS FOR A CLASS OF NONLINEAR SINGULAR PERTURBATION BOUNDARY VALUE PROBLEMS: Boundary layer-preserving methods for a class of nonlinear singular perturbation boundary value problems

Authors: Li, Xin Geng, Fazhan

Source: Journal of Applied Analysis & Computation. 13:1972-1982

Subject Terms: Method of contraction of the boundary for boundary value problems involving PDEs, nonlinear singularly perturbed problems, Singular perturbations for ordinary differential equations, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, boundary layers, Theoretical approximation in context of PDEs, reproducing kernel method, Numerical solution of singularly perturbed problems involving ordinary differential equations

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Boundedness and global existence in a higher-dimensional parabolic-elliptic-ODE chemotaxis-haptotaxis model with remodeling of non-diffusible attractant

Authors: Liu, Ling

Source: Journal of Mathematical Analysis and Applications. 549:129473

Subject Terms: global existence, Quasilinear parabolic equations, Cell movement (chemotaxis, etc.), Initial-boundary value problems for second-order parabolic systems, chemotaxis-haptotaxis, boundedness, remodeling of non-diffusible attractant, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, parabolic-elliptic-ODE

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Spectral instability of periodic peaked waves in the μ-b-family of Camassa-Holm equations: Spectral instability of periodic peaked waves in the \(\mu\)-\(b\)-family of Camassa-Holm equations

Authors: Haijing Song Ying Fu Hao Wang

Source: Journal of Differential Equations. 434:113311

Subject Terms: peakons, linearized operator, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Stability in context of PDEs, Initial value problems for nonlinear higher-order PDEs, spectral instability, \(\mu\)-\(b\)-family of the Camassa-Holm equations

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Access URL: https://zbmath.org/8034592
https://doi.org/10.1016/j.jde.2025.113311

Solvability of nonlinear pseudo‐parabolic equations involving generalized Caputo fractional derivatives: Solvability of nonlinear pseudo-parabolic equations involving generalized Caputo fractional derivatives

Authors: Nguyen Minh Dien Tran Quoc Viet Ravi P. Agarwal

Source: Mathematical Methods in the Applied Sciences. 47:11846-11873

Subject Terms: generalized Caputo fractional derivatives, Initial value problems for PDEs with pseudodifferential operators, differential equations, pseudo-parabolic, 0101 mathematics, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Fractional partial differential equations, Ultraparabolic equations, pseudoparabolic equations, etc, 01 natural sciences, fixed point theorems

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Access URL: https://zbmath.org/7996461
https://doi.org/10.1002/mma.9470

Continuous Dependence on Initial Data for Discontinuous Solutions of the Navier–Stokes Equations for One-Dimensional, Compressible Flow: Continuous dependence on initial data for discontinuous solutions of the Navier-Stokes equations for one-dimensional, compressible flow

Authors: David Hoff

Source: SIAM Journal on Mathematical Analysis. 27:1193-1211

Subject Terms: PDEs with low regular coefficients and/or low regular data, Error bounds for initial value and initial-boundary value problems involving PDEs, fractional Sobolev norms, Gas dynamics (general theory), error bounds, Navier-Stokes equations, 0101 mathematics, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, compressible fluid flow, discontinuous solutions, 01 natural sciences, interpolation, approximate solution

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Access URL: https://zbmath.org/938782
https://doi.org/10.1137/0527066
https://epubs.siam.org/doi/abs/10.1137/0527066

The initial-boundary value problem for the non-barotropic compressible Euler equations: structural-stability and data dependence: The initial-boundary value problem for the non-barotropic compressible Euler equations: Structural-stability and data dependence

Authors: BEIRAO DA VEIGA, HUGO

Source: Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 11:297-311

Subject Terms: structural stability, Boundary value problems for nonlinear first-order PDEs, 0101 mathematics, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics, Euler equations, 01 natural sciences, sharp data dependence, Second-order nonlinear hyperbolic equations, compressible inviscid fluids

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Access URL: http://www.numdam.org/item/AIHPC_1994__11_3_297_0.pdf
https://www.sciencedirect.com/science/article/abs/pii/S029414491630186X
http://ui.adsabs.harvard.edu/abs/1994AIHPC..11..297D/abstract
http://www.numdam.org/item/AIHPC_1994__11_3_297_0/
https://eudml.org/doc/78333
https://hdl.handle.net/11568/27148

On the Nature of Initial-Boundary Value Solutions for Dispersive Equations: On the nature of initial-boundary value solutions for dispersive equations

Authors: Bengt Fornberg Natasha Flyer

Source: SIAM Journal on Applied Mathematics. 64:546-564

Subject Terms: linear Schrödinger equation, Smoothness and regularity of solutions to PDEs, corner singularities, IBV solutions, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, 01 natural sciences, Singularity in context of PDEs, Boundary value problems for linear higher-order PDEs, dispersive equations, corner basis functions, 0101 mathematics, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, compatibility conditions, linearized KdV equation

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Access URL: https://zbmath.org/2024195
https://doi.org/10.1137/s0036139902415853

Non-intrusive reduced-order modeling for uncertainty quantification of space–time-dependent parameterized problems: Non-intrusive reduced-order modeling for uncertainty quantification of space-time-dependent parameterized problems

Authors: Xiang Sun Jung Il Choi

Source: Computers & Mathematics with Applications. 87:50-64

Subject Terms: polynomial chaos expansion, Spectral methods applied to problems in fluid mechanics, proper orthogonal decomposition, uncertainty quantification, Navier-Stokes equations for incompressible viscous fluids, Numerical methods for partial differential equations, boundary value problems, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, 0101 mathematics, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, 01 natural sciences, Finite element methods applied to problems in fluid mechanics, reduced-order modeling

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Access URL: https://zbmath.org/7325134
https://doi.org/10.1016/j.camwa.2021.01.015
https://www.sciencedirect.com/science/article/pii/S0898122121000250
https://doi.org/10.1016/j.camwa.2021.01.015
https://dblp.uni-trier.de/db/journals/cma/cma87.html#SunC21
https://yonsei.pure.elsevier.com/en/publications/non-intrusive-reduced-order-modeling-for-uncertainty-quantificati

Unboundedness of Solutions of an Initial-Boundary Value Problem for a Degenerate Nonlinear Parabolic Equation: Unboundedness of solutions of an initial-boundary value problem for a degenerate nonlinear parabolic equation

Authors: I. L. Pokrovskii

Source: Differential Equations. 37:834-838

Subject Terms: Integro-partial differential equations, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, blow up, modification of the Gronwall lemma, Asymptotic behavior of solutions to PDEs, 0101 mathematics, Degenerate parabolic equations, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, 01 natural sciences

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Access URL: https://link.springer.com/article/10.1023/A:1019246805034

An orderly linear PDE system with analytic initial conditions with a non-analytic solution: An orderly linear PDE system with analytic initial conditions with a non-analytic solution.

Authors: Lemaire, François Calcul Formel (CALFOR) Laboratoire d'Informatique Fondamentale de Lille (LIFL) et al.

Contributors: Lemaire, François Calcul Formel (CALFOR) Laboratoire d'Informatique Fondamentale de Lille (LIFL) et al.

Source: Journal of Symbolic Computation. 35:487-498

Subject Terms: [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], Gevrey series, Algebra and Number Theory, Riquier–Janet, Smoothness and regularity of solutions to PDEs, analyticity Riquier theorem, 0102 computer and information sciences, Differential algebra, PDE, Cauchy-Kovalevskaya theorems, 01 natural sciences, Computational Mathematics, orderly ranking, Characteristic sets, Cauchy–Kovalevskaya theorem, 0101 mathematics, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs

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Access URL: https://zbmath.org/1968933
https://doi.org/10.1016/s0747-7171(03)00017-8
https://dblp.uni-trier.de/db/journals/jsc/jsc35.html#Lemaire03
https://www.sciencedirect.com/science/article/pii/S0747717103000178
https://hal.archives-ouvertes.fr/hal-00545215
http://www.sciencedirect.com/science/article/pii/S0747717103000178

Life span of solutions with large initial data in a semilinear parabolic equation

Authors: Eiji Yanagida Noriko Mizoguchi

Source: Indiana University Mathematics Journal. 50:591-610

Subject Terms: Cauchy problem, Nonlinear parabolic equations, semilinear parabolic equation, 0101 mathematics, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, blow-up time, 01 natural sciences

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Access URL: https://zbmath.org/1679409
https://doi.org/10.1512/iumj.2001.50.1905
http://www.iumj.indiana.edu/IUMJ/fulltext.php?artid=1905&year=2001&volume=50

Parameter dependence of solutions of partial differential equations in spaces of real analytic functions

Authors: Paweł Domański José Bonet

Source: Proceedings of the American Mathematical Society. 129:495-503

Subject Terms: LB-space, Spaces of vector- and operator-valued functions, surjectivity of convolution and differential operators, Fréchet space, General theory of PDEs and systems of PDEs with constant coefficients, 0101 mathematics, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Topological invariants ((DN), (\(\Omega\)), etc.) for locally convex spaces, 01 natural sciences

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Access URL: https://www.ams.org/proc/2001-129-02/S0002-9939-00-05867-6/S0002-9939-00-05867-6.pdf
https://zbmath.org/1534696
https://doi.org/10.1090/s0002-9939-00-05867-6
https://www.ams.org/journals/proc/2001-129-02/S0002-9939-00-05867-6/home.html
https://documat.unirioja.es/servlet/articulo?codigo=726381
https://www.ams.org/proc/2001-129-02/S0002-9939-00-05867-6/S0002-9939-00-05867-6.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=726381

The Failure of Continuous Dependence on Initial data for the Navier–Stokes equations of Compressible Flow: The failure of continuous dependence on initial data for the Navier- Stokes equations of compressible flow

Authors: David Hoff Denis Serre

Source: SIAM Journal on Applied Mathematics. 51:887-898

Subject Terms: physical solutions, vacuum states, one-dimensional model of isentropic expansion of a compressible gas, momenta, Navier-Stokes equations, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics

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Access URL: https://zbmath.org/13862
https://doi.org/10.1137/0151043
https://epubs.siam.org/doi/10.1137/0151043
https://dl.acm.org/doi/10.1137/0151043
https://ui.adsabs.harvard.edu/abs/1991SJAM...51..887H/abstract

Existence, uniqueness, and dependence on a parameter of solutions of differential-functional equations with ordinary and partial derivatives

Authors: Ya. I. Bigun

Source: Ukrainian Mathematical Journal. 49:798-804

Subject Terms: Averaging method for ordinary differential equations, Cauchy problem, hyperbolic system, Partial functional-differential equations, existence, averaging method, uniqueness, 0101 mathematics, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, 01 natural sciences

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Access URL: https://link.springer.com/article/10.1007/BF02486461