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Di Ma & Yangjun Ma. (2023) On an incompressible inertial nematic electrolyte model of liquid crystal flow. Applicable Analysis 0:0, pages 1-34.
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Erhan Bayraktar, Qi Feng & Wuchen Li. (2023) Exponential Entropy Dissipation for Weakly Self-Consistent Vlasov–Fokker–Planck Equations. Journal of Nonlinear Science 34:1.
Crossref
Crossref
Antonio Agresti. (2023) Delayed blow-up and enhanced diffusion by transport noise for systems of reaction–diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations.
Crossref
Crossref
Chundi Liu & Shu Wang. (2022) Mixed Layer Problem and Quasineutral Limit of the Bipolar Drift-Diffusion Model with Different Mobilities. Results in Mathematics 77:5.
Crossref
Crossref
Julian Fischer, Katharina Hopf, Michael Kniely & Alexander Mielke. (2022) Global Existence Analysis of Energy-Reaction-Diffusion Systems. SIAM Journal on Mathematical Analysis 54:1, pages 220-267.
Crossref
Crossref
Mingying Zhong. (2022) Diffusion limit and the optimal convergence rate of the Vlasov-Poisson-Fokker-Planck system. Kinetic & Related Models 15:1, pages 1.
Crossref
Crossref
Klemens Fellner & Michael Kniely. (2021) Uniform convergence to equilibrium for a family of drift–diffusion models with trap‐assisted recombination and self‐consistent potential. Mathematical Methods in the Applied Sciences 44:17, pages 13040-13059.
Crossref
Crossref
Jae Yong Lee, Jin Woo Jang & Hyung Ju Hwang. (2021)
The model reduction of the Vlasov–Poisson–Fokker–Planck system to the Poisson–Nernst–Planck system
via
the Deep Neural Network Approach
. ESAIM: Mathematical Modelling and Numerical Analysis 55:5, pages 1803-1846.
Crossref
Crossref
Chia-Yu Hsieh, Tai-Chia Lin, Chun Liu & Pei Liu. (2020) Global existence of the non-isothermal Poisson–Nernst–Planck–Fourier system. Journal of Differential Equations 269:9, pages 7287-7310.
Crossref
Crossref
Jie Ding, Zhongming Wang & Shenggao Zhou. (2020) Structure-preserving and efficient numerical methods for ion transport. Journal of Computational Physics 418, pages 109597.
Crossref
Crossref
Philipp Holzinger & Ansgar Jüngel. (2020) Large-time asymptotics for a matrix spin drift-diffusion model. Journal of Mathematical Analysis and Applications 486:1, pages 123887.
Crossref
Crossref
Jingwei Hu & Xiaodong Huang. (2020) A fully discrete positivity-preserving and energy-dissipative finite difference scheme for Poisson–Nernst–Planck equations. Numerische Mathematik 145:1, pages 77-115.
Crossref
Crossref
Till D. Frank. 2020. Synergetics. Synergetics
149
182
.
David Kinderlehrer, Léonard Monsaingeon & Xiang Xu. (2016) A Wasserstein gradient flow approach to Poisson−Nernst−Planck equations. ESAIM: Control, Optimisation and Calculus of Variations 23:1, pages 137-164.
Crossref
Crossref
Hailiang Liu & Zhongming Wang. (2017) A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson–Nernst–Planck systems. Journal of Computational Physics 328, pages 413-437.
Crossref
Crossref
Till D. Frank. 2017. Encyclopedia of Complexity and Systems Science. Encyclopedia of Complexity and Systems Science
1
36
.
Alexander Mielke, Jan Haskovec & Peter A. Markowich. (2014) On Uniform Decay of the Entropy for Reaction–Diffusion Systems. Journal of Dynamics and Differential Equations 27:3-4, pages 897-928.
Crossref
Crossref
Jonathan Zinsl. (2015) Exponential convergence to equilibrium in a Poisson-Nernst-Planck-type system with nonlinear diffusion. Discrete and Continuous Dynamical Systems 36:5, pages 2915-2930.
Crossref
Crossref
Hao Wu, Tai-Chia Lin & Chun Liu. (2014) Diffusion Limit of Kinetic Equations for Multiple Species Charged Particles. Archive for Rational Mechanics and Analysis 215:2, pages 419-441.
Crossref
Crossref
Chia-Yu Hsieh & Tai-Chia Lin. (2015) Exponential Decay Estimates for the Stability of Boundary Layer Solutions to Poisson--Nernst--Planck Systems: One Spatial Dimension Case. SIAM Journal on Mathematical Analysis 47:5, pages 3442-3465.
Crossref
Crossref
Hailiang Liu & Zhongming Wang. (2014) A free energy satisfying finite difference method for Poisson–Nernst–Planck equations. Journal of Computational Physics 268, pages 363-376.
Crossref
Crossref
Christoph Kirsch & Sorin Mitran. (2012) Simulated annealing electro-photonic optimization of organic solar cells. Journal of Applied Physics 112:5.
Crossref
Crossref
Shu Wang & Ke Wang. (2009) Quasi-neutral Limit of the Drift-Diffusion Models for Semiconductors with PN-Junctions. Quasi-neutral Limit of the Drift-Diffusion Models for Semiconductors with PN-Junctions.
Andreas Prohl & Markus Schmuck. (2008) Convergent discretizations for the Nernst–Planck–Poisson system. Numerische Mathematik 111:4, pages 591-630.
Crossref
Crossref
Till D. Frank. 2009. Encyclopedia of Complexity and Systems Science. Encyclopedia of Complexity and Systems Science
5239
5265
.
Marco Di Francesco, Klemens Fellner & Peter A Markowich. (2008) The entropy dissipation method for spatially inhomogeneous reaction–diffusion-type systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464:2100, pages 3273-3300.
Crossref
Crossref
Marco Di Francesco & Marcus Wunsch. (2008) Large time behavior in Wasserstein spaces and relative entropy for bipolar drift-diffusion-Poisson models. Monatshefte für Mathematik 154:1, pages 39-50.
Crossref
Crossref
NICOLAS VAUCHELET. (2011)
DIFFUSIVE TRANSPORT OF PARTIALLY QUANTIZED PARTICLES: L
log
L SOLUTIONS
. Mathematical Models and Methods in Applied Sciences 18:04, pages 489-510.
Crossref
Crossref
HAO WU, PETER A. MARKOWICH & SONGMU ZHENG. (2011) GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR A SEMICONDUCTOR DRIFT-DIFFUSION-POISSON MODEL. Mathematical Models and Methods in Applied Sciences 18:03, pages 443-487.
Crossref
Crossref
Ling Hsiao & Shu Wang. (2006) Quasineutral limit of a time-dependent drift–diffusion–Poisson model for p-n junction semiconductor devices. Journal of Differential Equations 225:2, pages 411-439.
Crossref
Crossref
SHU WANG. (2011) QUASINEUTRAL LIMIT OF THE MULTI-DIMENSIONAL DRIFT-DIFFUSION-POISSON MODELS FOR SEMICONDUCTORS WITH PN-JUNCTIONS. Mathematical Models and Methods in Applied Sciences 16:04, pages 537-557.
Crossref
Crossref
Naoufel Ben Abdallah, Florian Méhats & Nicolas Vauchelet. (2004) A note on the long time behavior for the drift-diffusion-Poisson system. Comptes Rendus. Mathématique 339:10, pages 683-688.
Crossref
Crossref
T.D. Frank. (2004) Asymptotic properties of nonlinear diffusion, nonlinear drift‐diffusion, and nonlinear reaction‐diffusion equations. Annalen der Physik 516:7-8, pages 461-469.
Crossref
Crossref
A. Arnold, J. A. Carrillo, L. Desvillettes, J. Dolbeault, A. Jüngel, C. Lederman, P. A. Markowich, G. Toscani & C. Villani. 2004. Nonlinear Differential Equation Models. Nonlinear Differential Equation Models
35
43
.
CHRISTIAN SCHMEISER & SHU WANG. (2011) QUASINEUTRAL LIMIT OF THE DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS WITH GENERAL INITIAL DATA. Mathematical Models and Methods in Applied Sciences 13:04, pages 463-470.
Crossref
Crossref
V. Narayan & M. Willander. (2002)
Proposed experiments to grow nanoscale
junctions and modulation-doped quantum wires and dots
. Physical Review B 65:12.
Crossref
Crossref
V. Narayan & M. Willander. (2002) Monte Carlo simulation of controlled impurity diffusion in semiconductors using split gates. Physical Review B 65:7.
Crossref
Crossref