PDE 8015
PARTIAL DIFFERENTIAL EQUATIONS
QUESTION 3 [21 marks]
3. (a) Classify, reduce to normal form and hence solve
SUze + 10Ugy + 3Uyy = 0
(b) Classify, reduce to normal form and hence solve
Ure + 2Ugy + Uyy = 0
(c) Classify and reduce to normal form
Yo 2 Ure + LUyy = 0
JULY 2022
QUESTION 4 [20 marks]
4, (a) The temperature at one end of a 50cm long bar with insulated sides, is kept at 0°C
and that the other end is kept at 0°C' until steady-state condition prevails. The two
ends are then suddenly insulated and kept so. Find the temperature distribution
(b) Find the solution of the Cauchy problem
Ut — C’Ure = 0,
cER, t>0, u(z,0)=f(r), uw(z,0)=g9(z), cER.
(10)
End of Exam!