RENORMALIZED DISSIPATIVE SOLUTIONS OF SECOND ORDER DEGENERATE PARABOLIC BALANCE LAWS
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概要
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We introduce a new notion of renormalized dissipative solutions for the Cauchy problem of a second order degenerate parabolic balance law u_t + div F(u) =Δb(u) with locally Lipschitz-continuous flux F and L^1 data, and prove the equivalence of such solutions and renormalized entropy solutions in the sense of Bendahmane and Karlsen. The structure of renormalized dissipative solutions is flexible and suitable to deal with relaxation systems than the renormalized entropy scheme. The proof of our main theorem is based on the method of doubling variables established by Kruzkov.
- 2005-02-25
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- Renormalized Dissipative Solutions and Applications(Communication in commutative Banach algebras and several field of mathematics)
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- RENORMALIZED DISSIPATIVE SOLUTIONS OF SECOND ORDER DEGENERATE PARABOLIC BALANCE LAWS
- Uniqueness of Renormalized Solutions for Nonlinear Degenerate Problems (Viscosity Solutions of Differential Equations and Related Topics)
- Uniqueness of Renormalized Solutions of Degenerate Quasilinear Elliptic Equations