A Variational Calculus for Discontinuous Solutions of Systems of Conservation Laws
نویسندگان
چکیده
where F : IR 7→ IR and h : [0,+∞) × IR × IR 7→ IR are smooth maps. We assume that the system (1) is strictly hyperbolic, and that each characteristic field is either linearly degenerate or genuinely nonlinear in the sense of Lax [8]. Given a piecewise Lipschitz continuous solution u = u(t, x) of (1), we shall study the behavior of first-order variations of u, by defining a suitable class of “generalized tangent vectors” and determining their evolution in time. More precisely, consider a family of initial conditions u(0, x) = ū(x) depending on a small parameter ε, and assume that ū admits an expansion of the form ū(x) = ū(x) + εv̄(x) + o(ε). (2)
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