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Half‐space Fourier transform in application to non‐linear hyperbolic initial‐boundary‐value problem: low regularity solutions
Author(s) -
Łada Andrzej
Publication year - 1997
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/(sici)1099-1476(199712)20:18<1599::aid-mma913>3.0.co;2-w
Subject(s) - mathematics , mathematical analysis , initial value problem , boundary value problem , space (punctuation) , fourier transform , dirichlet distribution , nonlinear system , interval (graph theory) , dirichlet problem , dirichlet boundary condition
The Dirichlet initial‐boundary‐value problem in the half‐space ℝ t ×ℝ 3 + for a non‐linear hyperbolic system is studied. About the nonlinearity the null condition structure is imposed. Under the smallness conditions on the initial data the existence of low regularity solutions, on a given interval of time, is proved. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.