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Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.1. Second-Order Quasilinear Parabolic Equations
Equation(s):$\displaystyle \frac{\partial {w}}{\partial t} = a\frac{\partial}{\partial
x}\left(w^m\frac{\partial {w}}{\partial x}\right)+bw^{1-m}$.
Solution(s),
Transformation(s),
Integral(s)
:
Solution:\hfill\break
$\displaystyle w(x,t)=\left[\frac{(x+A)^2}{F(t)}+B|F(t)|^{-\frac m{m+1}}-
\frac{bm^2}{4a(m+1)}F(t)\right]^
{\frac{1}{m}},\quad F(t)=C-\frac{2a(m+2)}mt$,\hfill\break
where $A$, $B$, and $C$ are arbitrary constants.
Novelty:Material has been fully published elsewhere
References:R. Kersner, On some properties of weak solutions of quasilinear degenerate parabolic equations, Acta Math. Academy of Sciences, Hung., Vol. 32, No. 3--4, pp. 301--330, 1978.
Author/Contributor's Details
Last name:Vyazmina
First name:Elena
Middle(s) name:Andreevna
Country:Russia
City:Moscow
Affiliation:Ph.D student
Statistic information
Submission date:Thu 21 Dec 2006 13:07
Edits by author:0

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