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Fourth Order Diffusion Equations with Increasing Entropy.
- Source :
- Entropy; Jul2012, Vol. 14 Issue 7, p1127-1139, 13p, 4 Graphs
- Publication Year :
- 2012
-
Abstract
- The general quasi-linear autonomous fourth order diffusion equation u<subscript>t</subscript> = -[G(u)u<subscript /><subscript>xxx</subscript> + h(u, u<subscript>x</subscript>, u<subscript>xx</subscript>)]<subscript>x</subscript> with positive variable diffusivity G(u) and lower-order flux component h is considered on the real line. A direct algorithm produces a general class of equations for which the Shannon entropy density obeys a reaction-diffusion equation with a positive irreducible source term. Such equations may have any positive twice-differentiable diffusivity function G(u). The forms of such equations are the indicators of more general conservation equations whose entropy equation may be expressed in an alternative reaction-diffusion form whose source term, although reducible, is positive. [ABSTRACT FROM AUTHOR]
Details
- Language :
- Northern Sami
- ISSN :
- 10994300
- Volume :
- 14
- Issue :
- 7
- Database :
- Complementary Index
- Journal :
- Entropy
- Publication Type :
- Academic Journal
- Accession number :
- 79360155
- Full Text :
- https://doi.org/10.3390/e14071127