What are the underlying principles of how populations change over time? Two basic principles are involved, the idea of exponential growth and its ultimate control. The basics of population ecology ...

Consider an evolution equation with energy dissipation, ${\textstyle\frac{\partial}{\partial t}}y(x,t)=Ay(x,t)+By(x,t)$ on a bounded x-domain Ω, where By signifies a dissipative perturbation to an ...

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We derive estimates on the magnitude of non-adiabatic interaction between a Hamiltonian partial differential equation and a high-frequency nonlinear oscillator. Assuming spatial analyticity of the ...

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