A Class of Local Classical Solutions for the One-dimensional Perona-malik Equation
نویسندگان
چکیده
We consider the Cauchy problem for the one-dimensional PeronaMalik equation ut = 1− ux (1 + ux) 2 uxx in the interval [−1, 1], with homogeneous Neumann boundary conditions. We prove that the set of initial data for which this equation has a localin-time classical solution u : [−1, 1]× [0, T ] → R is dense in C1([−1, 1]). Here “classical solution” means that u, ut, ux and uxx are continuous functions in [−1, 1]× [0, T ].
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