Subject:PARTIAL DIFFERENTIAL EQUATION At the top there is equation (1) which u will use in part (a) of given question. Kindly use Use Cauchy characteristic method yo solve this full question(i.e part a&b) . Kindly solve this as soon as possible THANK YOU
Extracted text: u(r + ht,+,k) + u(x- h, t k)=u(x+ k, t+h) + u(x – k,t – h), ....eq() This is equation (1) which characteristic method Q. Consider the initial boundary value problems: x € (0, 7), t> 0, Ofu – 0u = 0, u(x, 0) = 0, x € (0, 7), initial data, t > 0, boundary values. dru(x, 0) = 1, %3D u(T, t) = 0, %3D u(0, t) = 0, %3D (a) Solve it using formula (1). (b) Is the resulting solution continuous? Is C' i.e, u(x, t) differentiable with du(x, t), d„u(x, t) continuous? Use Cauchy