Uniqueness of Solutions of the Derrida-Lebowitz-Speer-Spohn Equation and Quantum Drift-Diffusion Models

DOI10.1080/03605302.2013.823548zbMath1282.35011OpenAlexW2077297281MaRDI QIDQ5746979

Julian Fischer

Publication date: 11 February 2014

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2013.823548

zbMATH Keywords

DLSS equationsecond-order diffusion terms

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Initial-boundary value problems for higher-order parabolic equations (35K35) PDEs in connection with quantum mechanics (35Q40) Statistical mechanics of semiconductors (82D37) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Quasilinear parabolic equations (35K59)

Related Items (8)

An extension of the Derrida–Lebowitz–Speer–Spohn equation ⋮ Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation ⋮ Upper bounds on waiting times for the thin-film equation: the case of weak slippage ⋮ Long-time behavior of a fully discrete Lagrangian scheme for a family of fourth order equations ⋮ A convergent Lagrangian discretization for a nonlinear fourth-order equation ⋮ Global existence and exponential decay to equilibrium for DLSS-type equations ⋮ Well-posedness and convergence of a numerical scheme for the corrected Derrida-Lebowitz-Speer-Spohn equation using the Hellinger distance ⋮ A family of fourth-order \(q\)-logarithmic equations

Cites Work

• Existence of weak solution and semiclassical limit for quantum drift-diffusion model
• The bipolar quantum drift-diffusion model
• The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation
• Exponential time decay of solutions to a nonlinear fourth-order parabolic equation
• Elliptic partial differential equations of second order
• A multidimensional nonlinear sixth-order quantum diffusion equation
• First-order entropies for the Derrida-Lebowitz-Speer-Spohn equation
• Global Nonnegative Solutions of a Nonlinear Fourth-Order Parabolic Equation for Quantum Systems
• An algorithmic construction of entropies in higher-order nonlinear PDEs
• The Derrida–Lebowitz–Speer–Spohn Equation: Existence, NonUniqueness, and Decay Rates of the Solutions
• Dynamics of an anchored Toom interface
• Existence and positivity of solutions of a fourth‐order nonlinear PDE describing interface fluctuations
• Long-time behavior for a nonlinear fourth-order parabolic equation

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