Derive a solution to the initial-boundary value problem: Ut +u – Uzz = r(x, t), 0 0 u(0, t) = A(t), uz (1, t) = B(t), t>0 u(x, 0) = g(x), 0

Please solve

Extracted text: Derive a solution to the initial-boundary value problem: Ut +u – Uzz = r(x, t), 0< x="">< 1,="" t=""> 0 u(0, t) = A(t), uz (1, t) = B(t), t>0 u(x, 0) = g(x), 0 < x=""><1 hint:="" look="" for="" a="" function="" v(x,="" t)="" so="" that="" the="" function="" w(x,="" t)="" solves="" a="" problem="" of="" the="" form="" in="" question="" 2,="" where="" u(x,="" t)="v(x," t)="" +="" w(x,="" t).="" then="" use="" the="" result="" from="" question="">