2. Consider the generalized initial value problem Ut + cux 0, u(t, at) = f(t) where...

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2. Consider the generalized initial value problem Ut + cux 0, u(t, at) = f(t) where a and c +0 are given scalars, and f is a given continuous function. (a) Does this problem admit a unique solution for any value of a? Hint: draw the characteristics lines and the curve x(t) = at. (b) Solve the generalized IVP uz + 2ug = 0, u(t, t) = e=t. 2. Consider the generalized initial value problem Ut + cux 0, u(t, at) = f(t) where a and c +0 are given scalars, and f is a given continuous function. (a) Does this problem admit a unique solution for any value of a? Hint: draw the characteristics lines and the curve x(t) = at. (b) Solve the generalized IVP uz + 2ug = 0, u(t, t) = e=t.