A variational sheath model for gyrokinetic Vlasov-Poisson equations

We construct a stationary gyrokinetic variational model for sheaths close to the metallic wall of a magnetized plasma, following a physical extremalization principle for the natural energy. By considering a reduced set of parameters we show that our model has a unique minimal solution, and that the resulting electric potential has an infinite number of oscillations as it propagates towards the core of the plasma. We prove this result for the non linear problem and also provide a simpler analysis for a linearized problem, based on the construction of exact solutions. Some numerical illustrations show the well-posedness of the model after numerical discretization. They also exhibit the oscillating behavior.

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Asymptotic behavior of supercritical wave equations driven by colored noise on unbounded domains

Discrete and Continuous Dynamical Systems - Series B ◽

10.3934/dcdsb.2021223 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Bixiang Wang

Keyword(s):

Asymptotic Behavior ◽

Existence And Uniqueness ◽

Wave Equations ◽

Colored Noise ◽

Unbounded Domains ◽

Strichartz Estimates ◽

Well Posedness ◽

Natural Energy ◽

Random Attractors ◽

Supercritical Nonlinearity

<p style='text-indent:20px;'>This paper deals with the asymptotic behavior of the non-autonomous random dynamical systems generated by the wave equations with supercritical nonlinearity driven by colored noise defined on <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^n $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M2">\begin{document}$ n\le 6 $\end{document}</tex-math></inline-formula>. Based on the uniform Strichartz estimates, we prove the well-posedness of the equation in the natural energy space and define a continuous cocycle associated with the solution operator. We also establish the existence and uniqueness of tempered random attractors of the equation by showing the uniform smallness of the tails of the solutions outside a bounded domain in order to overcome the non-compactness of Sobolev embeddings on unbounded domains.</p>

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A Convex Variational Model for Learning Convolutional Image Atoms from Incomplete Data

Journal of Mathematical Imaging and Vision ◽

10.1007/s10851-019-00919-7 ◽

2019 ◽

Vol 62 (3) ◽

pp. 417-444

Author(s):

A. Chambolle ◽

M. Holler ◽

T. Pock

Keyword(s):

Image Reconstruction ◽

Inverse Problems ◽

Incomplete Data ◽

Variational Model ◽

Well Posedness ◽

Optimal Solutions ◽

Analytical Properties ◽

Numerical Performance ◽

Stability Results ◽

Continuous Setting

AbstractA variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is convex and allows for simultaneous image reconstruction and atom learning in a general, inverse problems context. Further, motivated by an improved numerical performance, also a semi-convex variant is included in the analysis and the experiments of the paper. For both settings, fundamental analytical properties allowing in particular to ensure well-posedness and stability results for inverse problems are proven in a continuous setting. Exploiting convexity, globally optimal solutions are further computed numerically for applications with incomplete, noisy and blurry data and numerical results are shown.

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Global well-posedness of strong solutions with large oscillations and vacuum to the compressible Navier-Stokes-Poisson equations subject to large and non-flat doping profile

Journal of Differential Equations ◽

10.1016/j.jde.2020.06.006 ◽

2020 ◽

Vol 269 (10) ◽

pp. 8468-8508

Author(s):

Shengquan Liu ◽

Xinying Xu ◽

Jianwen Zhang

Keyword(s):

Strong Solutions ◽

Doping Profile ◽

Navier Stokes ◽

Well Posedness ◽

Poisson Equations

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On a Nonlinear Mixed Problem for a Parabolic Equation with a Nonlocal Condition

Axioms ◽

10.3390/axioms10030181 ◽

2021 ◽

Vol 10 (3) ◽

pp. 181

Author(s):

Abdelkader Djerad ◽

Ameur Memou ◽

Ali Hameida

Keyword(s):

Iterative Process ◽

Linear Problem ◽

Nonlocal Condition ◽

A Priori ◽

A Priori Estimate ◽

Well Posedness ◽

Analysis Method ◽

Integral Conditions ◽

Priori Estimate ◽

Mixed Problems

The aim of this work is to prove the well-posedness of some linear and nonlinear mixed problems with integral conditions defined only on two parts of the considered boundary. First, we establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense using a functional analysis method. Then by applying an iterative process based on the obtained results for the linear problem, we establish the existence, uniqueness and continuous dependence of the weak solution of the nonlinear problem.

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Global well-posedness of compressible bipolar Navier-Stokes-Poisson equations

Acta Mathematica Sinica English Series ◽

10.1007/s10114-011-0238-x ◽

2011 ◽

Vol 28 (5) ◽

pp. 925-940 ◽

Cited By ~ 5

Author(s):

Yi Quan Lin ◽

Cheng Chun Hao ◽

Hai Liang Li

Keyword(s):

Navier Stokes ◽

Well Posedness ◽

Poisson Equations

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The well-posedness theory for Euler–Poisson fluids with non-zero heat conduction

Journal of Hyperbolic Differential Equations ◽

10.1142/s0219891614500210 ◽

2014 ◽

Vol 11 (04) ◽

pp. 679-703

Author(s):

Jiang Xu

Keyword(s):

Heat Conduction ◽

Besov Spaces ◽

Hyperbolic Systems ◽

Type Inequality ◽

Classical Solutions ◽

Well Posedness ◽

Poisson Equations ◽

The Cauchy Problem ◽

Critical Besov Spaces ◽

Temperature Equation

This paper is devoted to the Euler–Poisson equations for fluids with non-zero heat conduction, arising in semiconductor science. Due to the thermal effect of the temperature equation, the local well-posedness theory by Xu and Kawashima (2014) for generally symmetric hyperbolic systems in spatially critical Besov spaces does not directly apply. To deal with this difficulty, we develop a generalized version of the Moser-type inequality by using Bony's decomposition. With a standard iteration argument, we then establish the local well-posedness of classical solutions to the Cauchy problem for intial data in spatially Besov spaces.

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Corrigendum to “Global well-posedness of strong solutions with large oscillations and vacuum to the compressible Navier-Stokes-Poisson equations subject to large and non-flat doping profile” [J. Differ. Equ., 269(10) (2020) 8468–8508]

Journal of Differential Equations ◽

10.1016/j.jde.2021.02.014 ◽

2021 ◽

Author(s):

Shengquan Liu ◽

Xinying Xu ◽

Jianwen Zhang

Keyword(s):

Strong Solutions ◽

Doping Profile ◽

Navier Stokes ◽

Well Posedness ◽

Poisson Equations

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Fast Healthcare Interoperability Resources (FHIR®) Representation of Medication Data Derived from German Procedure Classification Codes (OPS) Using Identification of Medicinal Products (IDMP) Compliant Terminology

German Medical Data Sciences: Bringing Data to Life - Studies in Health Technology and Informatics ◽

10.3233/shti210074 ◽

2021 ◽

Author(s):

Julian Sass ◽

Susanne Zabka ◽

Andrea Essenwanger ◽

Josef Schepers ◽

Martin Boeker ◽

...

Keyword(s):

Minimal Solution ◽

Use Case ◽

Medicinal Products ◽

University Hospitals ◽

Electronic Documentation ◽

Amount Of Substance ◽

The Core ◽

Core Dataset ◽

Procedure Classification ◽

Unit Of Measurement

Electronic documentation of medication data is one of the biggest challenges associated with digital clinical documentation. Despite its importance, it has not been consistently implemented in German university hospitals. In this paper we describe the approach of the German Medical Informatics Initiative (MII) towards the modelling of a medication core dataset using FHIR® profiles and standard-compliant terminologies. The FHIR profiles for Medication and MedicationStatement were adapted to the core dataset of the MIl. The terminologies to be used were selected based on the criteria of the ISO-standard for the Identification of Medicinal Products (IDMP). For a first use case with a minimal medication dataset, the entries in the medication chapter of the German Procedure Classification (OPS codes) were analyzed and mapped to IDMP-compliant medication terminology. OPS data are available at all German hospitals as they are mandatory for reimbursement purposes. Reimbursement-relevant encounter data containing OPS medication procedures were used to create a FHIR representation based on the FHIR profiles MedicationStatement and Medication. This minimal solution includes – besides the details on patient and start-/end-dates – the active ingredients identified by the IDMP-compliant codes and – if specified in the OPS code – the route of administration and the range of the amount of substance administered to the patient, using the appropriate unit of measurement code. With FHIR, the medication data can be represented in the data integration centers of the MII to provide a standardized format for data analysis across the MII sites.

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