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Solving u_y + a(x,y) u_x = 0 for function a(x,y) that yields no solution 
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Sep2211, 04:16 PM

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Hi. I am taking a PDE class and struggling a little. The professor gave us this problem to practice:
Find a function a = a(x,y) continuous such that for the equation $u_y + a(x,y) u_x = 0 $ there does not exist a solution in all of $R^2$ for any nonconstant initial value defined on the hyperplane ${(x,0)}$ I thought that in order to find such a function I needed to make the hyperplane characteristic at all points, but that got me nowhere. Please help me find a direction. Any help would be much appreciated! Thanks in advance! 


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