Existence and uniqueness of PDEs

daniel_8775
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Hello,

I have a PDE:

3*u_x + 2*u_y = 0, and I am interested in determining initial values such that there is a unique solution, there are multiple solutions, and there are no solutions at all.

What theorem(s)/techniques would be of use to me for something like this?

Regards,
Dan
 
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You should be thinking of the method of characteristics.

The general solution to your equation is u=f(2x-3y)
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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