Some progress on the hydrocode convergence problem

摘要

We prove an existence and uniqueness theorem for a solution (vu) to the initial-boundary-value problem ∂u∂t+∂∂μ[P(v)]−δ2∂2u∂μ2=0, ∂v∂t=∂v∂μ, u(t,μ)=b(t,μ)forμ ∈ {0,l}, u(0,μ)= u0(μ), v(0,μ)=v0(mu;), and demonstrate convergence to vu of solutions of a discretized version of (A).