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Global classical solutions to partially dissipative quasilinear hyperbolic systems with weaker restrictions on wave interactions
Author(s) -
Qu Peng
Publication year - 2013
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.2701
Subject(s) - dissipative system , dissipation , degenerate energy levels , mathematics , initial value problem , mathematical analysis , cauchy problem , hyperbolic partial differential equation , partial differential equation , physics , thermodynamics , quantum mechanics
A kind of partially dissipative quasilinear hyperbolic systems in which a part of equations possesses the strict dissipation and the others are weakly linearly degenerate are discussed. Under some weaker hypotheses on the interactions between two parts of equations, it is proved that for any given initial data with small W 1,1 and C 1 norms, the corresponding Cauchy problem admits a unique C 1 global classical solution. Copyright © 2012 John Wiley & Sons, Ltd.