Journal
NONLINEARITY
Volume 20, Issue 3, Pages 685-712Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0951-7715/20/3/007
Keywords
-
Categories
Ask authors/readers for more resources
There has been much investigation of higher order nonlinear degenerate equations of the form h(t) = (M( h) (delta H/delta h)(x))(x), whereM is a specified function and H is the quadratic first order energy functional 1/2 integral h(x)(2) dx. 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 H-p = integral( h(x)(2))(p/2) dx for p not equal 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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available