Can anyone solve question 1 and 3? step by step please

 

 

MATH3403 Assigment 1
This assignment is worth 4% of the total assessment. Late penalties are listed in the
profile. If you hand it in late, you must hand it to the assignment box (Level 4) AND email
your tutor saying that you have done so.
Each problem is going to be marked from 0-10 with 6 points going to the procedure
(including neatness and clarity) and 4 for the final answer. The total score for the assignment
is 30 points.
1. Solve the equation aux + buy + u = 0 with Cauchy data u(s) = e−s along the straight
lines (x(s), y(s)) = (cs, ds). The solution breaks down for a particular combination
of a, b, c and d. Describe the combination geometrically and explain it in terms of
characteristic curves.
2. Consider the equation yux − xuy = 0 (y > 0). Check for each of the following initial
conditions wheter the problem is solvable. If it is solvable, find a solution, If it is not,
explain why
(a) u(x, 0) = x2
(b) u(x, 0) = x
3. Consider the equation (1 − v 2 )uxx + 2(1 + v 2 )uxy + (1 − v 2 )uyy = 0 where v is a constant
real parameter with |v| < 1. After proving that this is an hyperbolic PDE show that
its general solution (without Cauchy data) is similar to the general solution of the wave
equation (uxx − v 2 uyy ) with v equal to the propagation speed. 1

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Status NEW Posted 20 Apr 2017 04:04 AM My Price 8.00

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