Consider the function v(x, t) that satisfies the PDE Vx+8x³, vt=0 for x > 0 and t> 0, and the initial condition v(x,0) =

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Consider The Function V X T That Satisfies The Pde Vx 8x Vt 0 For X 0 And T 0 And The Initial Condition V X 0 1 (81.99 KiB) Viewed 40 times

Consider the function v(x, t) that satisfies the PDE Vx+8x³, vt=0 for x > 0 and t> 0, and the initial condition v(x,0) = 0. (a) Apply the Laplace transform in t to the PDE and derive an expression for V/V, where V(x, s) = L(v(x, t)) is the Laplace transform in t of v. Var & P (b) Integrate to find V in the form V(x, s) = C(s)g(x, s), where C(s) comes from the constant of integration and g(0, s) = 1. g(x, s) = BB (c) If v satisfies the boundary condition v(0, t) = 5t then find C(s). C(s) = (d) If v(x, t) = f(t - A)u(t - A), where u is the unit step function, then find A(x) and f(t). A(x) = f(t) = & P