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Results tagged with linear-pde
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user 25510
Questions about linear partial differential equations. Often used in combination with the top-level tag ap.analysis-of-pdes.
3
votes
How to find the eigenvalues equation of this PDE problem
Your coefficients are piecewise constant, which allows you to write the general solution of your differential equation. First write the general solutions on each interval where they are constant. This …
- 91.8k
9
votes
How to trap a particle without using potential field which is infinity at some point? (quant...
Trapping means that an eigenfunction has compact support. For locally bounded potential this is impossible, because of uniqueness theorem. Suppose for simplicity that our system is 1-dimensional. Then …
- 91.8k
4
votes
Accepted
Solution of Poisson equation vanishing at the boundary of any order
No. Take any $u$ which is not zero, but compactly supported in $\Omega$. Then
define $f=\Delta u$; it will be also compactly supported, and non-zero.
- 91.8k