Cauchy problem and periodic homogenization for nonlocal Hamilton–Jacobi equations with coercive gradient terms
2019 ◽
Vol 150
(6)
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pp. 3028-3059
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AbstractThis paper deals with the periodic homogenization of nonlocal parabolic Hamilton–Jacobi equations with superlinear growth in the gradient terms. We show that the problem presents different features depending on the order of the nonlocal operator, giving rise to three different cell problems and effective operators. To prove the locally uniform convergence to the unique solution of the Cauchy problem for the effective equation we need a new comparison principle among viscosity semi-solutions of integrodifferential equations that can be of independent interest.
2001 ◽
Vol 45
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pp. 1015-1037
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2007 ◽
Vol 04
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pp. 771-795
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Vol 05
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pp. 127-145
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Vol 6
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pp. 289-304
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Vol 62
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pp. 391-397
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Vol 21
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pp. 1850025
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