An Example of Global Classical Solution for the Perona-Malik Equation
نویسندگان
چکیده
منابع مشابه
An example of global classical solution for the Perona-Malik equation
We consider the Cauchy problem for the Perona-Malik equation ut = div ( ∇u 1 + |∇u|2 ) in an open set Ω ⊆ R, with Neumann boundary conditions. It is well known that in the one-dimensional case this problem does not admit any global C solution if the initial condition u0 is transcritical, namely when |∇u0(x)| − 1 is a sign changing function in Ω. In this paper we show that this result cannot be ...
متن کاملGradient estimates for the Perona-Malik equation
We consider the Cauchy problem for the Perona-Malik equation ut = div ( ∇u 1 + |∇u|2 ) in a bounded open set Ω ⊆ R, with Neumann boundary conditions. If n = 1, we prove some a priori estimates on u and ux. Then we consider the semi-discrete scheme obtained by replacing the space derivatives by finite differences. Extending the previous estimates to the discrete setting we prove a compactness re...
متن کاملPerona-Malik equation and its numerical properties
This work concerns the Perona-Malik equation, which plays essential role in image processing. The first part gives a survey of results on existance, uniqueness and stability of solutions, the second part introduces discretisations of equation and deals with an analysis of discrete problem. In the last part I present some numerical results, in particular with algorithms applied to real images.
متن کاملA Class of Local Classical Solutions for the One-dimensional Perona-malik Equation
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 func...
متن کاملAn Analysis of the Perona-Malik Scheme
We investigate how the Perona-Malik scheme evolves piecewise smooth initial data in one dimension. By scaling a natural parameter that appears in the scheme in an appropriate way with respect to the grid size, we obtain a meaningful continuum limit. The resulting evolution can be seen as the gradient flow for an energy, just as the discrete evolutions are gradient flows for discrete energies. I...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2011
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605302.2010.542672