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(a) Assume 𝐄=(E^1, E^2, E^3) and 𝐁=(B^1, B^2, B^3) solve Maxwell's equations { 𝐄t=curl𝐁, 𝐁t=-curl𝐄 div𝐁=div𝐄=0. Show 𝐄t t-Δ𝐄=0, 𝐁t t-Δ𝐁=0 (b) Assume that 𝐮=(u^1, u^2, u^3) solves the evolution equations of linear elasticity 𝐮t t-μΔ𝐮-(λ μ) D(div 𝐮)=0 in ℝ^3 ×(0, ∞) Show w:=div 𝐮 and 𝐰:=curl 𝐮 each solve wave equations, but with differing speeds of propagation. | Numerade
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