TY - JOUR
T1 - Sufficient conditions for local existence via Glimm's scheme for large BV data
AU - Schochet, Steven
PY - 1991/2
Y1 - 1991/2
N2 - Using Glimm's scheme, sufficient conditions are derived for the global existence of a weak solution to a strictly hyperbolic genuinely nonlinear system of partial differential equations in one space dimension when the initial data is a small BV perturbation of a solvable Riemann problem. By using the finite propagation speed of the system, this yields a local existence theorem for arbitrary BV initial data that satisfies the above-mentioned conditions at all large jumps. The case of linearly degenerate fields is also treated, and the results are applied to the p-system and to the 1-D nonisentropic γ-gas-law Euler equations.
AB - Using Glimm's scheme, sufficient conditions are derived for the global existence of a weak solution to a strictly hyperbolic genuinely nonlinear system of partial differential equations in one space dimension when the initial data is a small BV perturbation of a solvable Riemann problem. By using the finite propagation speed of the system, this yields a local existence theorem for arbitrary BV initial data that satisfies the above-mentioned conditions at all large jumps. The case of linearly degenerate fields is also treated, and the results are applied to the p-system and to the 1-D nonisentropic γ-gas-law Euler equations.
UR - http://www.scopus.com/inward/record.url?scp=0001304520&partnerID=8YFLogxK
U2 - 10.1016/0022-0396(91)90124-R
DO - 10.1016/0022-0396(91)90124-R
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AN - SCOPUS:0001304520
SN - 0022-0396
VL - 89
SP - 317
EP - 354
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -