# Questions tagged [pde]

Questions on partial (as opposed to ordinary) differential equations.

14,158 questions
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### Proving that a hyperbolic PDE admits a weak solution

I've been given a hyperbolic differential equation. The question is the following: Prove that the above problem admits a weak solution (Hint: write an equation satisfied by $v=e^{\lambda t}u$, then ...
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### Deriving the residual error for finite elements.

I am using the following set of notes for adaptive finite elements (https://www.ruhr-uni-bochum.de/num1/files/lectures/AdaptiveFEM.pdf) and am trying to go through the error calculations on page 29&...
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### Studying Differential Equations without Physics Experience [on hold]

As I get closer to becoming a graduate student, I'm trying to figure out what my interests in math are and which one I would like to pursue and do research in. Recently, I've been thinking about going ...
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### Why is this eigenvalue problem solved by $\phi(r) = J_v(\alpha r)$

I can't seem to see how the bessel function $J_v(ar)$ solves the problem. The eigenvalue problem has an $\alpha^ 2\phi(r)$ term Ive tried writing $x = \alpha r$ in the expression for $J$ but cant ...
I have a question on a fundamental property of harmonic functions. Let $\Omega \subset \mathbb{R}^d$ be a domain. We define $H^{1}(\Omega)$ by \begin{align*} H^{1}(\Omega)=\{u \in L^{2}(\Omega,m) \...
I'm trying to re-solve the governing equations in hydraulic fracturing modeling  \frac{\partial q}{\partial x} + \frac{2hC}{\sqrt{t-\tau(x)}} + \frac{\partial A}{\partial t} = 0 , \qquad 0<x&...