Please show each step in the solution process so that I can follow your
solution method.
Consider the diffusion equation:
on the time-dependent domain
where a is a constant. We wish to solve the initial and boundary value
problem having
. Thus, u is prescribed as a function of time on the left boundary
that moves at a constant speed a.
a) Introduce the transformation of variables
and solve the resulting problem by Laplace transforms.
b) Calculate the appropriate Green’s function for the problem in x, t
variables and
rederive the solution using this.
This problem is taken from Partial Differential Equations: Analytical
Solution Techniques, by J. Kevorkian. (Prob. 1.4.7)
Mathematics Homework Solutions
#33393
PDE with Time-Dependent Domain
Please see the attached file for the fully formatted problems.
Consider the diffusion equation:
on the time-dependent domain
where a is a constant. We wish to solve the initial and boundary value problem having
for and a prescribed . Thus, u is prescribed as a function of time on the left boundary that moves at a constant speed a.
a) Introduce the transformation of variables
and solve the resulting problem by Laplace transforms.
b) Calculate the appropriate Green's function for the problem in x, t variables and
rederive the solution using this.
This problem is taken from Partial Differential Equations: Analytical Solution Techniques, by J. Kevorkian. (Prob. 1.4.7)
A PDE with Time-Dependent Domain is investigated using convolution and the the Dirac distribution. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.
What is this?
By OTA - Overall OTA Rating
Marius Brebenel, PhD - 4.9/5
Purchase Cost Now
$2.19 CAD (was ~$31.92)
Included in Download
- Plain text response
- Attached file(s):
- P33393.doc
Why you can trust BrainMass.com
- Your Information is Secure
- Best Online Academic Help Service
- Students find real academic Success
- Dirac Delta Function - Please see the attached file for the fully formatted problem. Express d(xa) in terms of the Dirac delta "function" d(x), where a is a non-zero constant.
- Wave Packet Trains : Express in Terms of Dirac Delta Function - Wave Packet Trains : Express in Terms of Dirac Delta Function Please see the attached file for the fully formatted problems.
- Representation of the Dirac Delta Function - Please see the attached file for the fully formatted problems. Show that is a representation of the Dirac S-function. Discussion: Let and let f(x) be a function which is piecewise continuou ...
- Periodic Functions via Convolution - Please see the attached file for the fully formatted problems. "Periodic Function via Convolution" Consider the periodic train of Dirac delta "functions" f(x) =.... with real period .... (a) FI ...
- Fourier Transforms, Gaussian and Ricker Wavelets and Waveforms and Dirac Delta Function - See attached file for full problem description. Question 5 is also a proof, but requires a further matlab plot.
