# Tagged Questions

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### Finding solution to a unidirectional nonlinear wave equation

I can do the parts a), b) and c) and find that in part c) that the condition in which the solution will break down is when $1+tf'(x-tu)=0$ However I am unable to part d) I tried ...
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### Symbol of self-adjoint pseudodifferential operator

It seems that the following result should hold, but I can't find it explicitly anywhere. If $A=A^*$ is a properly supported pseudodifferential operator, does this imply that ...
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### Laplace's equation boundary conditions

I am supposed to determine a solution from the following boundary conditions in a rectangular area $V$. $f(0,y)=f(x,a) = f(x,0)=0$ and $f(b,y) = C\ sin(\frac{\pi}{a}y)$, for $a,b \in \mathbb{R}$. I ...
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### Greens function of 1-d forced wave equation

[ORIGINAL PROBLEM] You are given hat the Green's function $g(x,t,\xi, \phi)$ is $\frac{\partial^2g}{\partial t^2} - \frac{\partial^2g}{\partial x^2}=\delta(t-\tau)\delta(x-\xi)$ with ...
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### what is the solution of this question on partial differential equation

what is the solution of this $$\frac{1}{D^2_x-D^2_y}\sin(x-y)$$ please solve, should I move using $\exp(x-y)$ or any other method is there to solve this for particular integral
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### is this intengral bounded?

Im just stuck beacause I dont know if this integral in bounded, I was trying to make a change of variable but I cant get to anything: (edited what need is that f is bounded for a fixed x) ...
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### Sign of Laplacian at critical points of $\mathbb R^n$

Suppose we are in $\mathbb R^n$. What can we say about the sign of $\Delta u(\vec x)$ if u($\vec x$) has a local max/min at $\vec x$? I've tried looking at the reverse of the second partial derivative ...
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### How to separate $x^2X''v+xX'v+Xv_{yy}+x^2Xv_{zz} = 0$

I have the following partial differential equation: $$x^2X''v+xX'v+Xv_{yy}+x^2Xv_{zz} = 0,$$ where $X = X(x)$ and $v = v(y,z)$. How to separate it? Thank you for any help! From the book: ...
I'm reading about separation of variables in my Fourier series book and there is one requirement in a problem I don't understand. Here it is: I don't understand, why can't the $\sqrt{-A}$ take a ...