Global existence of weak discontinuous solutions to the Cauchy problem with small BV initial data for quasilinear hyperbolic systems | Zendy

Wang Libin | Zendy

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Global existence of weak discontinuous solutions to the Cauchy problem with small BV initial data for quasilinear hyperbolic systems

Author(s) -

Wang Libin

Publication year - 2014

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.3123

Subject(s) - mathematics , uniqueness , initial value problem , bounded function , norm (philosophy) , cauchy problem , hyperbolic partial differential equation , mathematical analysis , cauchy distribution , weak solution , partial differential equation , political science , law

In this paper, we study the Cauchy problem for quasilinear hyperbolic system with a kind of non‐smooth initial data. Under the assumption that the initial data possess a suitably small bounded variation norm, a necessary and sufficient condition is obtained to guarantee the existence and uniqueness of global weak discontinuous solution. Copyright © 2014 John Wiley & Sons, Ltd.

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