# Questions tagged [partial-differential-equations]

Questions on partial (as opposed to ordinary) differential equations - equations involving partial derivatives of one or more dependent variables with respect to more than one independent variables.

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### A PDE with mixed derivative

How should one go about solving an equation of the form $$\frac{\partial^2 u}{\partial x \partial y} + x \frac{\partial u}{\partial y} = y$$ Do I need to use characteristics, or integrate first?
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### Proving that solution one and 2 are equivalent of given PDE

I found the solution of the given PDE by two methods but I want to check whehter both the solutions are the same or not. can some help me?
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### Homogeneous semi-infinite wave equation with inhomogeneous boundary and initial conditions

On page 115 of the third edition of Logan's Applied Partial Differential Equations, the reader is asked to solve the following: $$u_{tt} = u_{xx}, \,\,\: x,t>0$$ $$u(0,t) = \sin t ,\,\,\: t\ge 0$$...
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### Parabolic linear PDE with non-homogenous Neumann boundary condition.

Let $\Omega \subset \mathbb{R}^n$ be an open bounded set with lipschitz boundary, $T>0$, $f \in L^2(0,T;L^2(\Omega))$, $g \in L^2(0,T;H^{\frac{1}{2}}(\Omega))$ and $h \in H^1(\Omega).$ I'm trying ...
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### Momentum integral in axisymmetric turbulent flow

Context: I am trying to derive an equation given in a Journal of Fluid Mechanics paper (2.2). It deals with the analysis of an axisymmetric turbulent wake where cylindrical coordinate system has been ...
Using separation of variables find solutions to the equation $3u_{xy}=u$. My attempt: $u(x,y)=X(x)Y(y) \Rightarrow u_{xy}=X'(x)Y'(y) \Rightarrow 3X'Y'=XY$ From what I've seen and read, it's necessary ...