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Received October 30, 2019; Accepted March 5, 2020; Published April 3, 2020
Abstract. In this paper, we present existence and uniqueness results of entropic solutions for nonlinear problems. First, we introduce the notion of good solutions and their relationships with weak solutions. Then we study a parabolic problem with the space variable dependent absorption, for which we demonstrate the existence and uniqueness of entropic solutions. We also present a particular application to show the competitive results for image inpainting.
How to Cite this Article:
Fatma Zohra Nouri, Uniqueness and existence results for a partial differential equation in image inpainting, Communications in Optimization Theory, Vol. 2020 (2020), Article ID 7, pp. 1-17.