Subcritical Hamilton–Jacobi fractional equation in
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| Authors: | Tomasz Dlotko Maria B Kania |
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| Affiliation: | Institute of Mathematics, Silesian University, 40‐007 Katowice, Bankowa 14, Poland |
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| Abstract: | Solvability of Cauchy's problem in  for fractional Hamilton–Jacobi equation (1.1) with subcritical nonlinearity is studied here both in the classical Sobolev spaces and in the locally uniform spaces. The first part of the paper is devoted to the global in time solvability of subcritical equation (1.1) in locally uniform phase space, a generalization of the standard Sobolev spaces. Subcritical growth of the nonlinear term with respect to the gradient is considered. We prove next the global in time solvability in classical Sobolev spaces, in Hilbert case. Regularization effect is used there to guarantee global in time extendibility of the local solution. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | psuedodifferential operators Hamilton– Jacobi equation fractional diffusion locally uniform spaces |
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