On the Hölder regularity of the weak solution to a drift–diffusion system with pressure

2018 ◽  
Vol 57 (6) ◽  
Author(s):  
Qianyun Miao ◽  
Liutang Xue
Keyword(s):  
Weak Solution ◽  
Diffusion System ◽  
Hölder Regularity ◽  
Drift Diffusion ◽  
Holder Regularity

scholarly journals The relaxation limit of bipolar fluid models

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nuno J. Alves ◽  
Athanasios E. Tzavaras
Keyword(s):  
Weak Solution ◽  
Smooth Solution ◽  
Vacuum Solution ◽  
Relative Energy ◽  
Diffusion System ◽  
Fluid Models ◽  
Energy Identity ◽  
Poisson System ◽  
Drift Diffusion ◽  
Friction Regime

<p style='text-indent:20px;'>This work establishes the relaxation limit from the bipolar Euler-Poisson system to the bipolar drift-diffusion system, for data so that the latter has a smooth solution. A relative energy identity is developed for the bipolar fluid models, and it is used to show that a dissipative weak solution of the bipolar Euler-Poisson system converges in the high-friction regime to a strong and bounded away from vacuum solution of the bipolar drift-diffusion system.</p>

scholarly journals Characterization of Pointwise Hölder Regularity

1997 ◽  
Vol 4 (4) ◽  
pp. 429-443 ◽  
Author(s):  
Patrik Andersson
Keyword(s):  
Hölder Regularity ◽  
Holder Regularity

scholarly journals On a Drift–Diffusion System for Semiconductor Devices

2016 ◽  
Vol 17 (12) ◽  
pp. 3473-3498 ◽  
Author(s):  
Rafael Granero-Belinchón
Keyword(s):  
Semiconductor Devices ◽  
Diffusion System ◽  
Drift Diffusion

A NUMERICAL ANALYSIS OF A REACTION–DIFFUSION SYSTEM MODELING THE DYNAMICS OF GROWTH TUMORS

2010 ◽  
Vol 20 (05) ◽  
pp. 731-756 ◽  
Author(s):  
VERÓNICA ANAYA ◽  
MOSTAFA BENDAHMANE ◽  
MAURICIO SEPÚLVEDA
Keyword(s):  
Weak Solution ◽  
Numerical Analysis ◽  
Numerical Scheme ◽  
System Modeling ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Existence Of Weak Solutions ◽  
Early Tumor ◽  
Volume Method

We consider a reaction–diffusion system of 2 × 2 equations modeling the spread of early tumor cells. The existence of weak solutions is ensured by a classical argument of Faedo–Galerkin method. Then, we present a numerical scheme for this model based on a finite volume method. We establish the existence of discrete solutions to this scheme, and we show that it converges to a weak solution. Finally, some numerical simulations are reported with pattern formation examples.

scholarly journals Hölder regularity for degenerate parabolic equations with variable exponents

2022 ◽  
Vol 40 ◽  
pp. 1-19
Author(s):  
Hamid EL Bahja
Keyword(s):  
Weak Solutions ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Hölder Regularity ◽  
Variable Exponents ◽  
Young’S Inequality ◽  
Scaling Method ◽  
Degenerate Parabolic ◽  
Young's Inequality ◽  
Holder Regularity

In this paper, we discuss a class of degenerate parabolic equations with variable exponents. By  using the Steklov average and Young's inequality, we establish energy and logarithmicestimates for solutions to these equations. Then based on the intrinsic scaling method, we provethat local weak solutions are locally continuous.

scholarly journals Hölder regularity for the spectrum of translation flows

2021 ◽  
Vol 8 ◽  
pp. 279-310
Author(s):  
Alexander I. Bufetov ◽  
Boris Solomyak
Keyword(s):  
Hölder Regularity ◽  
Holder Regularity
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