Physical Sciences and Mathematics Commons^™

Blue Whale And Krill Populations Modeling, Li Zhang

CODEE Journal

We present an intriguing topic in an undergraduate mathematical modeling course where predator-prey models are taught to our students. We describe modeling activities and the use of technology that can be implemented in teaching this topic. Through modeling activities, students are expected to use the numerical and graphical methods to observe the qualitative long-term behavior of predator and prey populations. Although there are other choices of predators and prey, we find that using blue whales and krill as predator and prey, respectively, would be most beneficial in strengthening our students' awareness of protecting endangered species and its impact on climate …

Existence And Uniqueness For A Variational Hyperbolic System Without Resonance, Peter W. Bates, Alfonso Castro

All HMC Faculty Publications and Research

In this paper, we study the existence of weak solutions of the problem

□u + ∇G(u) = f(t,x) ; (t,x) є Ω ≡ (0,π)x(0,π)

u(t,x) = 0 ; (t,x) є ∂Ω

where □ is the wave operator ∂²/∂t² - ∂²/∂x², G: Rⁿ→R is a function of class C² such that ∇G(0) = 0 and f:Ώ→R^n is a continuous function having first derivative with respect to t in (L₂,(Ω))ⁿ and satisfying

f(0,x) = f(π,x) = 0

for all x є [0,π].