On a New Family of Degenerate Parabolic Equations | Zendy

Süleyman Ulusoy | Zendy

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On a New Family of Degenerate Parabolic Equations

Author(s) -

Süleyman Ulusoy

Publication year - 2008

Publication title -

applied mathematics research express

Language(s) - English

Resource type - Journals

eISSN - 1687-1200

pISSN - 1687-1197

DOI - 10.1093/amrx/abm010

Subject(s) - degenerate energy levels , dissipation , nonlinear system , mathematics , entropy (arrow of time) , mathematical physics , statistical physics , pure mathematics , mathematical analysis , physics , thermodynamics , quantum mechanics

which was first derived in (Ulusoy, Nonlinearity 20 (2007): 685–712). We prove results on the regularity of non-negative solutions. In Ulusoy, an entropy dissipation–entropy estimate was provided for the p = 3 and n = 2 case using the energy functional Kq := ∫ hx hq dx. Here, we extend our calculations to include various other p and n values. After establishing some results on the support properties of solutions, we finally complete the analysis of the long-time behavior of non-negative weak solutions.

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