All Questions
Tagged with eigenvector ap.analysis-of-pdes
7 questions
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Are eigenfunctions of the Dirichlet problem for the Laplace equation uniformly bounded?
Let $Q\subset \mathbb R^n$ be a bounded domain with boundary $\partial Q\in C^\infty$ and $\varphi_1,\varphi_2,\ldots$ are eigenfunctions of the Dirichlet problem for the Laplace equation in $Q$ ...
- 2,715
3
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Are Neumann Laplacian eigenfunctions in $C(\overline{\Omega})$?
Consider that $u\in H^1(\Omega)$ with $\Delta u\in L^2(\Omega)$ (in the distributional sense) such that for some $\lambda>0$ we have that:
$$\begin{cases} \Delta u(x)=\lambda u(x), & x\in\Omega\...
- 1,759
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Eigenvalues and eigenvectors of non-symmetric elliptic operators
We know that the operator $A=\Delta$ with domain $D(A)=\{u\in W^{2, 2}(\Omega): u=0 \ \ \text{on } \partial\Omega\}$ (say $\Omega$ is a bounded nice domain) has eigenvalues $\lambda_1>\lambda_2\ge \...
- 11
10
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Can a vector-function $v:\mathbb{R}^n\to \mathbb{R}^n$ be an eigenvector of its own Jacobian matrix?
Good morning,
I've came across this question, which has been puzzling me for some days. Suppose we are given a vector-valued function $v:\mathbb{R}^n\to \mathbb{R}^n$, $v(x)=\left( v_1(x),\dots, v_n(...
- 311
6
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Density of squares of radial eigenfunctions
The eigenfunctions of the Laplace operator on the disc can be written in polar coordinates as $f(r,\theta)=R_{nk}(r)e^{ik\theta}$, where $k\in\mathbb Z$ and $n\in\mathbb N$ and the radial function is $...
- 8,086
3
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406
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Asymptotic behavior of the Dirichlet-Laplacian eigenvalues [closed]
I found in a math book http://www.cambridge.org/dz/academic/subjects/mathematics/differential-and-integral-equations-dynamical-systems-and-co/introduction-partial-differential-equations?format=PB&...
- 617
6
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Analytical solution to a Linear advection-reaction PDE
I am looking for an analytical solution for the linear PDE
$(1)\qquad\qquad \qquad f_t+ A f_x + B f = 0, $
Where $A$ and $B$ are constant matrices and $f=f(x,t)$ is a vector.
Clearly each one of $...
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