Trouble with dirac delta in R^2

In summary, a distribution F in R^2 that satisfies (Dx) F(x,t) = t*Delta(x) is not t*H(x) as in R. The ODE u' + u = t*Delta(x) + Delta''(x) can be solved by multiplying both sides by exp(x) and integrating.
  • #1
obomov2
3
0
Find a distribution F in R^2 that satisfies (Dx) F(x,t) = t*Delta(x)
It is apperantly not t*H(x) as in R.

* is multiplication, D is dirac delta, H is Heavyside , (Dx) is derivation with respect to x (in the sense of distributions)

Sorry for not using Latex.

Indeed I am trying to solve following ODE for u(t,x) :
u' + u = t*Delta(x) + Delta'' (x)
 
Physics news on Phys.org
  • #2
obomov2 said:
Find a distribution F in R^2 that satisfies (Dx) F(x,t) = t*Delta(x)
It is apperantly not t*H(x) as in R.

why not?

obomov2 said:
Indeed I am trying to solve following ODE for u(t,x) :
u' + u = t*Delta(x) + Delta'' (x)

multiply both sides by exp(x) to get d/dx(exp(x)u) on the left hand side and integrate.
 

FAQ: Trouble with dirac delta in R^2

1. What is the Dirac delta function in two dimensions?

The Dirac delta function, denoted as δ(x,y), is a mathematical function used in two-dimensional space to represent a point mass or impulse. It is defined as zero everywhere except at the origin (x=0, y=0) where it has an infinite value, but with an area of 1 under its curve.

2. How is the Dirac delta function used in two-dimensional space?

The Dirac delta function is often used as a mathematical tool to simplify calculations involving point masses, such as in electromagnetism or fluid dynamics. It can also be used to represent a point source of energy or a point charge in two-dimensional space.

3. What are the properties of the Dirac delta function in two dimensions?

The Dirac delta function in two dimensions has similar properties to the one-dimensional version, including symmetry, scaling, and shifting. Additionally, it satisfies the integral property where its integral over any area containing the origin is equal to 1.

4. What are some applications of the Dirac delta function in two dimensions?

The Dirac delta function is commonly used in physics and engineering, such as in the study of electromagnetic fields, signal processing, and fluid dynamics. It is also used in image processing and computer graphics to represent point objects or singularities.

5. What are some challenges when working with the Dirac delta function in two dimensions?

One challenge is the interpretation of the infinite value at the origin, which may lead to mathematical inconsistencies if not properly handled. Another challenge is the need for careful handling when integrating or manipulating equations involving the Dirac delta function, as it can lead to incorrect results if not done correctly.

Similar threads

I Integrating with the Dirac delta distribution
Replies
9
Views
2K
I On the approximate solution obtained through Euler's method
Replies
1
Views
2K
I What Are Common Misconceptions About the Dirac Delta Function?
Replies
25
Views
2K
I Assuming boundary conditions when integrating by parts
Replies
1
Views
2K
Sifting property of a Dirac delta inverse Mellin transformation
Replies
31
Views
3K
Mellin transform of Dirac delta function ##\delta(t-a)##
Replies
3
Views
2K
I Derivation of Lax-Wendroff finite volume scheme
Replies
1
Views
2K
Derivative of Dirac Delta function
Replies
5
Views
12K
I Fourier transform of Dirac delta
Replies
3
Views
2K
Can the Dirac Delta Impulse be eliminated in this differential equation?
Replies
5
Views
3K

Hot Threads

Recent Insights

Back
Top