Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I want to ask a question about the eigenvalue problem (EVP) and the initial value problem (IVP).

Let's say we are solving this linear equation [itex]\frac{\partial u}{\partial t}=\mathcal{L}u[/itex], the operator L is dependent on some parameters like Reynolds number.

I first check the eigenvalue of the equation at a specific parameter set.

My question is if the eigenvalue at this specific parameter is positive (meaning the system is unstable), now I solved the IVP counterpart [itex]\frac{u^{n+1}-u^n}{dt}=\mathcal{L}u[/itex] with an ARBITRARY initial condition, will this initial condition amplifies over all the time history (especially at the early phase, because I know asymptotically the system is governed by the positive eigenvalue)?

Thanks in advance

Jo

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Eigenvalue problem and initial-value problem?

**Physics Forums | Science Articles, Homework Help, Discussion**