TY - JOUR
T1 - Scalar conservation laws on a half-line
T2 - A parabolic approach
AU - Bank, Miriam
AU - Ben-Artzi, Matania
PY - 2010/3
Y1 - 2010/3
N2 - The initial-boundary value problem for the (viscous) nonlinear scalar conservation law is considered, ut∈=∈u xx∈, xε ℝ+=(0,∞), 0≤t≤T, ∈≥0, u∈(x,o)=u0(x), u∈(0,t)=g(t).The flux f(ξ) ∈ C2() is assumed to be convex (but not strictly convex, i.e. f″(ξ)< 0). It is shown that a unique limit u = lim→0 uε exists. The classical duality method is used to prove uniqueness. To this end parabolic estimates for both the direct and dual solutions are obtained. In particular, no use is made of the Krukov entropy considerations.
AB - The initial-boundary value problem for the (viscous) nonlinear scalar conservation law is considered, ut∈=∈u xx∈, xε ℝ+=(0,∞), 0≤t≤T, ∈≥0, u∈(x,o)=u0(x), u∈(0,t)=g(t).The flux f(ξ) ∈ C2() is assumed to be convex (but not strictly convex, i.e. f″(ξ)< 0). It is shown that a unique limit u = lim→0 uε exists. The classical duality method is used to prove uniqueness. To this end parabolic estimates for both the direct and dual solutions are obtained. In particular, no use is made of the Krukov entropy considerations.
KW - Duality method
KW - Initial-boundary value problem
KW - Scalar conservation law
KW - Uniqueness
KW - Zero viscosity limit
UR - http://www.scopus.com/inward/record.url?scp=77951670099&partnerID=8YFLogxK
U2 - 10.1142/S0219891610002086
DO - 10.1142/S0219891610002086
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AN - SCOPUS:77951670099
SN - 0219-8916
VL - 7
SP - 165
EP - 189
JO - Journal of Hyperbolic Differential Equations
JF - Journal of Hyperbolic Differential Equations
IS - 1
ER -