6533b858fe1ef96bd12b5750
RESEARCH PRODUCT
An algorithmic construction of entropies in higher-order nonlinear PDEs
Ansgar JüngelDaniel Matthessubject
Partial differential equationDiffusion equationApplied MathematicsMathematical analysisGeneral Physics and AstronomyStatistical and Nonlinear PhysicsStrong Subadditivity of Quantum EntropySobolev inequalityBinary entropy functionNonlinear systemEntropy (energy dispersal)Mathematical PhysicsJoint quantum entropyMathematicsdescription
A new approach to the construction of entropies and entropy productions for a large class of nonlinear evolutionary PDEs of even order in one space dimension is presented. The task of proving entropy dissipation is reformulated as a decision problem for polynomial systems. The method is successfully applied to the porous medium equation, the thin film equation and the quantum drift–diffusion model. In all cases, an infinite number of entropy functionals together with the associated entropy productions is derived. Our technique can be extended to higher-order entropies, containing derivatives of the solution, and to several space dimensions. Furthermore, logarithmic Sobolev inequalities can be obtained.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-01-31 | Nonlinearity |