In this paper, the author obtains the existence and uniqueness of weak solutions of the Cauchy problem for a quasilinear equation of conservation type with memory ut +f(u)x +a∗ψ(u) = 0, u(0,x) = u0(x), in one space variable. The main additional hypothesesareψ(0)=0,ψ′ >0and(−1)na(n) ≥0forn=0,1,2.
Weak solutions of a conservation law with memory
rosella Sampalmieri
1997-01-01
Abstract
In this paper, the author obtains the existence and uniqueness of weak solutions of the Cauchy problem for a quasilinear equation of conservation type with memory ut +f(u)x +a∗ψ(u) = 0, u(0,x) = u0(x), in one space variable. The main additional hypothesesareψ(0)=0,ψ′ >0and(−1)na(n) ≥0forn=0,1,2.File in questo prodotto:
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