Unformatted text preview: τ as the parameter on the initial line, show that unless f ( τ ) < − c , no breaking occurs. 9. Consider the one-dimensional Form oF Euler’s equations For isentropic ﬂow and assume that the pressure p is a constant. The equations reduce to ρ t + ρu x + uρ x = 0 u t + uu x = 0 Let u ( x, 0) = f ( x ) and ρ ( x, 0) = g ( x ). By ±rst solving the equation For u and then the equation For ρ , obtain the implicit solution u = f ( x − ut ) ρ = g ( x − ut ) 1 + tf ( x − ut ) 246...
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- Fall '08
- Implicit Differentiation, Constant of integration, Boundary value problem