SOLUTION OF STOCHASTIC HEAT EQUATION
We consider heat distribution problem in a bar of finite length under random heat source. The phenomenon is modelled as one dimensional stochastic heat equation. Analytically the equation is written as an abstract Cauchy problem in an appropriate Hilbert space. It is solved via semigroup theory t...
Saved in:
| Main Author: | |
|---|---|
| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/44323 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| id |
id-itb.:44323 |
|---|---|
| spelling |
id-itb.:443232019-10-10T10:23:53ZSOLUTION OF STOCHASTIC HEAT EQUATION Robby Indonesia Final Project stochastic heat equation, abstract Cauchy problem, semigroup theory INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/44323 We consider heat distribution problem in a bar of finite length under random heat source. The phenomenon is modelled as one dimensional stochastic heat equation. Analytically the equation is written as an abstract Cauchy problem in an appropriate Hilbert space. It is solved via semigroup theory to get a mild solution. The solution of this problem is simulated using Python. The numpy package is used for the vector and matrix computation, and the matplotlib package is used for plotting. We observe disintegration of smoothing effect of the heat equation by the presence of white noise modelled after the random heat source; the solution to the stochastic heat equation loses in regularity. text |
| institution |
Institut Teknologi Bandung |
| building |
Institut Teknologi Bandung Library |
| continent |
Asia |
| country |
Indonesia Indonesia |
| content_provider |
Institut Teknologi Bandung |
| collection |
Digital ITB |
| language |
Indonesia |
| description |
We consider heat distribution problem in a bar of finite length under random heat source. The phenomenon is modelled as one dimensional stochastic heat equation. Analytically the equation is written as an abstract Cauchy problem in an appropriate Hilbert space. It is solved via semigroup theory to get a mild solution.
The solution of this problem is simulated using Python. The numpy package is used for the vector and matrix computation, and the matplotlib package is used for plotting. We observe disintegration of smoothing effect of the heat equation by the presence of white noise modelled after the random heat source; the solution to the stochastic heat equation loses in regularity.
|
| format |
Final Project |
| author |
Robby |
| spellingShingle |
Robby SOLUTION OF STOCHASTIC HEAT EQUATION |
| author_facet |
Robby |
| author_sort |
Robby |
| title |
SOLUTION OF STOCHASTIC HEAT EQUATION |
| title_short |
SOLUTION OF STOCHASTIC HEAT EQUATION |
| title_full |
SOLUTION OF STOCHASTIC HEAT EQUATION |
| title_fullStr |
SOLUTION OF STOCHASTIC HEAT EQUATION |
| title_full_unstemmed |
SOLUTION OF STOCHASTIC HEAT EQUATION |
| title_sort |
solution of stochastic heat equation |
| url |
https://digilib.itb.ac.id/gdl/view/44323 |
| _version_ |
1822926839097589760 |