Register to reply

Maths Biology - linear instability

by Auron87
Tags: biology, instability, linear, maths
Share this thread:
Auron87
#1
Oct29-07, 09:03 AM
P: 12
1. The problem statement, all variables and given/known data

Given the linear diffusion equation with a linear source term,

[tex]\frac{\partial u}{\partial t} =\frac{\partial^2u}{\partial x^2} + au[/tex]

where a is a positive constant and inital data u(x,0) = u0(x) use a linear instability analysis to show u identically equal to 0 is always unstable no matter how small a > 0.

2. Relevant equations

3. The attempt at a solution

To be honest I really don't know where to start. We've seen a similar example without the 'au' term and I'm struggling to follow through that. We've been told that the differential equation should come to

{sigma}*u = -k^2*u + au

but I'm not sure how to get to there. From this I can tell that sigma could be positive or negative whereas in his example, sigma was always negative which meant that u identically equal to 0 was always stable. I'm genuinely unsure of where to go with this problem.
Thanks for any help.
Phys.Org News Partner Science news on Phys.org
Bees able to spot which flowers offer best rewards before landing
Classic Lewis Carroll character inspires new ecological model
When cooperation counts: Researchers find sperm benefit from grouping together in mice

Register to reply

Related Discussions
Be 8 nuclear instability General Physics 2
More WAIS (W. Antarctica) instability? Earth 1
Undergrad projects in maths and biology General Discussion 4
Can I get into a molecular biology graduate program without a biology bachelors Academic Guidance 3
Linear transformation in Maths Introductory Physics Homework 6