Large time behavior for a viscous Hamilton-Jacobi equation with Neumann boundary condition |
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Authors: | Sa?¨d Benachour Simona Dabuleanu |
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Institution: | Institut Elie Cartan UMR 7502 UHP-CNRS-INRIA, BP 239 F-54506 Vandoeuvre-lès-Nancy, France |
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Abstract: | We prove the existence and the uniqueness of strong solutions for the viscous Hamilton-Jacobi equation: with Neumann boundary condition, and initial data μ0, a continuous function. The domain Ω is a bounded and convex open set with smooth boundary, a∈R,a≠0 and p>0. Then, we study the large time behavior of the solution and we show that for p∈(0,1), the extinction in finite time of the gradient of the solution occurs, while for p?1 the solution converges uniformly to a constant, as t→∞. |
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Keywords: | 35K55 35K60 35B33 35B35 35B65 |
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