# Questions tagged [greens-function]

This tag is for questions about a Green's function which is the impulse response of an inhomogeneous differential equation defined on a domain, with specified initial conditions or boundary conditions.

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### I'm looking for resources that involve concretely taking Lebesgue integral of functions (non-axiomatic and computation focused)

I want to practice finding the Lebesgue integrals of certain functions. My source of inspiration is integrating Dirac delta functions and anything relating to differential equations like Green's ...
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### Undergraduate references on Sturm-Liouville Theory and Green's Functions

Does anybody know of any clear treatments of Sturm-Liouville theory and Greens functions suitable to accompany undergraduate courses on the subject material? Thanks.
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### Interpreting Green's function in Evans' Partial Differential Equations

Pictures below is from Evans' Partial Differential Equations. $U\subset \mathbb R^n$ is open, bounded. And $\nu$ is the normal vector of $\partial U$. I want to get the last red box from the first ...
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### Needing reference on fundamental set of solution for differential equation on vector fields

Let $L$ be a differential operator on functions $f:\mathbb{R}^N\mapsto\mathbb{R}$. Under some assumptions, we can find the solutions of $Lf = g$ where $f$ and $g$ are both functions from $\mathbb{R}^N$...
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### Trouble on transforming a PDE into an ODE and solving it

I have encountered an issue in a PDE (A Green's function actually). I am solving it in (d+1)-dimensions and I use Poincare coordinates, meaning I have a dimension "z" and I also have d-...
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### Solution of the parabolic PDE using Green's function

Green's function for the parabolic PDE is defined as: $$\Delta G(\vec{x},t,\vec{\xi},\theta)=\delta(\vec{x}-\vec{\xi},t-\theta)$$ Where $G$ satifies the homogeneous initial and boundary conditions. ...
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### Numerical integration with modified Bessel function of second kind

I am working with the so-called screened Poisson PDE, whose solutions in two-dimensions are given in terms of the modified Bessel function of the second kind, $K_0$, for Dirichlet boundary conditions ...
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### What is monopole, mathematically?

$\newcommand{\realset}{\mathbb{R}}$ $\newcommand{\lapop}[1]{\nabla^{2} #1}$ $\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}$ $\newcommand{\shift}[1]{\tau_{#1}}$ Recently, I wrote down the ...
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### What justifies the $\epsilon \rightarrow 0$ limit in the domain of this integral?

I am following these notes on Green's function for Poisson's equation, which are based on Evan's PDE book. Let $\Omega \subset \mathbb{R}^n$ be open and bounded. Let $u \in C^2(\overline{\Omega})$ be ...
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### How to get/determine the Green's Function?

I want to determine the Green's function of $$t y^{\prime \prime}(t)+y^{\prime}(t)=t, \quad y(1)=y(e)=0.$$ I have even solved the ODE with the initial conditions, but I do not know how to determine ...
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### Question about the fomula of Green function of Laplacian on closed manifold.

I'm reading a paper which said that the Green function for $\left(-\Delta_g\right)^m$ on $2m-dimension$ closed manifold is of the form \tag{1} G_y(x)=\frac{2}{\Lambda_1} \log \frac{1}{d_g(x, y)}+\...
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### How to set up integral for solution to PDE using Green's function?

I've found Green's function, the problem is I've never done the integration part to find the solution for a 2-D problem or higher before, so I'd like a little guidance for setting up the integral. The ...
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### How to derive a key equation in Sturm-Liouville Theory

Recently bombed a quiz on Sturm-Liouville theory and orthogonal polynomials in my math methods for physics class, and I'm trying to go through the chapter on the theory and plug up the holes in the ...
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