Entropy-dissipating finite-difference schemes for nonlinear fourth-order parabolic equations
DOI10.3934/dcdsb.2020234zbMath1483.65129arXiv2001.03742OpenAlexW3046239747MaRDI QIDQ2033561
Marcel Braukhoff, Ansgar Jüngel
Publication date: 17 June 2021
Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2001.03742
Nonlinear parabolic equations (35K55) PDEs in connection with fluid mechanics (35Q35) Thin fluid films (76A20) Lubrication theory (76D08) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Statistical mechanics of semiconductors (82D37) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Initial value problems for higher-order parabolic equations (35K30) Other free boundary flows; Hele-Shaw flows (76D27) Higher-order parabolic equations (35K25) PDEs in connection with statistical mechanics (35Q82)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Entropic Ricci curvature bounds for discrete interacting systems
- Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics
- Entropy-dissipating semi-discrete Runge-Kutta schemes for nonlinear diffusion equations
- A convergent Lagrangian discretization for a nonlinear fourth-order equation
- A gradient flow scheme for nonlinear fourth order equations
- Well-posedness for a class of fourth order diffusions for image processing
- Convex entropy decay via the Bochner-Bakry-Emery approach
- Discrete Beckner inequalities via the Bochner-Bakry-Emery approach for Markov chains
- Entropy-stable and entropy-dissipative approximations of a fourth-order quantum diffusion equation
- Structure preserving approximation of dissipative evolution problems
- Spectral gap estimates for interacting particle systems via a Bochner-type identity
- Long-time behavior of a finite volume discretization for a fourth order diffusion equation
- An algorithmic construction of entropies in higher-order nonlinear PDEs
- Entropy dissipative one‐leg multistep time approximations of nonlinear diffusive equations
- The Derrida–Lebowitz–Speer–Spohn Equation: Existence, NonUniqueness, and Decay Rates of the Solutions
- Existence and positivity of solutions of a fourth‐order nonlinear PDE describing interface fluctuations
- On a Fourth-Order Degenerate Parabolic Equation: Global Entropy Estimates, Existence, and Qualitative Behavior of Solutions
- Fluctuations of a stationary nonequilibrium interface
- Discrete variational derivative method—A structure-preserving numerical method for partial differential equations
- Low‐curvature image simplifiers: Global regularity of smooth solutions and Laplacian limiting schemes
- Positivity-Preserving Numerical Schemes for Lubrication-Type Equations
