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The Cauchy problem for ut=Δu+|∇u| |
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| Authors: | Brian H. Gilding Mohammed Guedda |
| Affiliation: | a Department of Mathematics and Statistics, Sultan Qaboos University, Al Khod, Oman b Faculty of Mathematics and Computer Science, University of Picardie ‘Jules Verne,’ Amiens, France c Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Hungary |
| Abstract: | With q a positive real number, the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces. In that context it is known as the generalized deterministic KPZ equation. The paper is concerned with the initial-value problem for the equation under the assumption that the initial-data function is bounded and continuous. Results on the existence, uniqueness, and regularity of solutions are obtained. |
| Keywords: | Surface growth KPZ equation Viscous Hamilton-Jacobi equation Nonlinear Parabolic Existence Uniqueness Regularity |
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