Süleyman Ulusoy 2007 Nonlinearity 20 685 doi:10.1088/0951-7715/20/3/007
A new family of higher order nonlinear degenerate parabolic equations
Süleyman Ulusoy
Show affiliationsRecommended by A L Bertozzi
There has been much investigation of higher order nonlinear degenerate equations of the form 
where M is a specified function and H is the quadratic first order energy functional 
. The energy functional arises in many physical models, but is not universal among higher order parabolic equations. Recent investigations have motivated the study of other energy functionals, such as 
for p ≠ 2. We undertake such a study here, proving the existence of weak solutions for appropriate boundary conditions, nonnegativity and positivity properties of solutions. Moreover, an entropy dissipation–entropy estimate for solutions of this equation is obtained. Support properties and long time behaviour of solutions are also discussed for various cases.
- Programs are available at www.math.kth.se/~gaidash/Programs/belt_bounds.tar.bz2
- PACS
- MSC
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35K25 General theory of higher-order, parabolic equations
35K55 Nonlinear PDE of parabolic type
35B40 Asymptotic behavior of solutions
35K65 Parabolic partial differential equations of degenerate type
- Subjects
- Dates
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Issue 3 (March 2007)
Received 24 August 2006, in final form 5 December 2006
Published 31 January 2007
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A new family of higher order nonlinear degenerate parabolic equations
Süleyman Ulusoy 2007 Nonlinearity 20 685
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