*Accepted Paper*

**Inserted:** 7 may 2003

**Last Updated:** 13 nov 2006

**Journal:** Comm. Partial Differential Equations

**Year:** 2003

**Abstract:**

We prove that every function $u:\re^{2}\to\re$ of class $C^{1}$,
satisfying the Perona-Malik equation
$$u_{{t}=\left}(\frac{u_{{x}}{1+u}_{{x}}^{{2}}\right)}_{{x}$$
}
for every $(x,t)\in\re^{2}$, is a stationary affine solution,
\ie\ of the form $u(x,t)=ax+b$, where $a$ and $b$ are suitable real
constants.

**Keywords:**
Perona-Malik equation, anisotropic diffusion, entire solution, forward-backward parabolic equation

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