Using fourier and laplace transform to solve PDE

[cyw1984]

PDE is type of heat equation.

Many book only gives an example of solving heat equation using Fourier transform.
An exercise asks me to solve it for using Fourier and laplace transform:

In the heat equation, we'd take the Fourier transform with respect to x for
each term in the equation. How to combine it with using Fourier and laplace transform

Can anyone suggest some example and notes to me??

 

[cyw1984]

umum...the question mention us to use Fourier and laplace transform. Is there mention us to use Fourier transform with respect to t (t>0) and then inverse Fourier transform to solve the solution; Separately, solve the question using laplace transform with respect to x -\infty< x < \infty and then inverse laplace transform?

Can there combines two transformation in one??
What is the result compared with two method??

 

[AiRAVATA]

It's all the way around... The Fourier transform is defined in \mathbb{R}, while the Laplace transform is defined in \mathbb{R}^+, so you have to take the Fourier transform in space and the Laplace transform in time. That way, you will land with a polinomial equation in two variables, which will give you some sort of dispersion relation.

 

[cyw1984]

It's all the way around... The Fourier transform is defined in \mathbb{R}, while the Laplace transform is defined in \mathbb{R}^+, so you have to take the Fourier transform in space and the Laplace transform in time. That way, you will land with a polinomial equation in two variables, which will give you some sort of dispersion relation.

O...
you mean that it must need to do it independent in two times??

What information will give in this type of question??