Abstract
We study here solutions of inviscid Burgers equation with a stochastic initial value with homogeneous and independent increments without positive jumps. We define the notion of intrinsic statistical solution of this evolution equation and show that a family (X (t); t ≥ 0) of homogeneous Lévy processes is an intrinsic statistical solution of Burgers equation if and only if the exponent functions ψ (t, w) satisfy the differential equation: ∂tψ = i ψ ∂wψ. The existence of such solutions follows then from the examination of that last equation. The case of a brownian initial condition is made explicit.
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