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Subcritical Hamilton–Jacobi fractional equation in R N
Author(s) -
Dlotko Tomasz,
Kania Maria B.
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3241
Subject(s) - mathematics , sobolev space , regularization (linguistics) , mathematical analysis , hilbert space , initial value problem , nonlinear system , generalization , banach space , evolution equation , pure mathematics , physics , quantum mechanics , artificial intelligence , computer science
Solvability of Cauchy's problem inR Nfor 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.