Energy-transport systems for optical lattices: Derivation, analysis, simulation

DOI10.1142/S021820251850015XzbMath1387.35369arXiv1704.02845OpenAlexW2605689510MaRDI QIDQ4603534

Marcel Braukhoff, Ansgar Jüngel

Publication date: 15 February 2018

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.02845

zbMATH Keywords

finite differencesexistence of weak solutionsdegenerate equationsoptical latticeenergy-transport modelsquadratic gradient

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Kinetic theory of gases in equilibrium statistical mechanics (82B40) Boltzmann equations (35Q20) Quasilinear parabolic equations (35K59)

Related Items (3)

Global analytic solutions of the semiconductor Boltzmann-Dirac-Benney equation with relaxation time approximation ⋮ Existence analysis of a degenerate diffusion system for heat-conducting gases ⋮ Semiconductor Boltzmann-Dirac-Benney equation with a BGK-type collision operator: existence of solutions vs. ill-posedness

Cites Work

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• On the Cauchy problem for \(u_t= \Delta\log u\) in higher dimensions
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• Existence analysis for a simplified transient energy-transport model for semiconductors
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• Bose-Condensed Gases at Finite Temperatures
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• On a hierarchy of macroscopic models for semiconductors
• Global Weak Solutions to Compressible Navier–Stokes Equations for Quantum Fluids
• Asymptotic Behavior of the Solution to a 3-D Simplified Energy-Transport Model for Semiconductors

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