Existence of global bounded weak solutions to nonsymmetric systems of Keyfitz–Kranzer type

By Yun-guang Lu. 2011

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In this paper, we study the global L∞ solutions for the Cauchy problem of nonsymmetric system (1.1) of Keyfitz–Kranzer type. When n=1, (1.1) is the Aw–Rascle traffic flow model. First, we introduce a new flux approximation to obtain a lower bound ρe,δ⩾δ>0 for the parabolic system generated by adding “artificial viscosity” to the Aw–Rascle system. Then using the compensated compactness method with the help of L1 estimate of we,δ(⋅,t)x we prove the pointwise convergence of the viscosity solutions under the general conditions on the function P(ρ), which includes prototype function P(ρ)=1γργ+A, where γ∈(−1,0)∪(0,∞), A is a constant. Second, by means of BV estimates on the Riemann invariants and the compensated compactness method, we prove the global existence of bounded entropy weak solutions for the Cauchy problem of general nonsymmetric systems (1.1).

Subfields: Applied Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/742e6f961e9507cf542e40715ec2f22003befd40