2015/03/18 by Dieter Graß, Dieter Grass, Grass, Dieter +2 · 1 citation
Environmental Science · Mathematics · Physics and Astronomy · #35B32 #49J20 #49N90 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #Ecosystem dynamics and resilience #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #math.AP #math.OC #msc:35B32 #msc:49J20 #msc:49N90
paper · pdf · doi:10.48550/arxiv.1503.05438
updated, and some typos fixed, removed "Scenario 2"
openalex publication_date 2015/03/18 · arxiv created 2015/06/10 · arxiv updated 2015/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a numerical framework to treat infinite time horizon spatially distributed optimal control problems via the associated canonical system derived by Pontryagin's Maximum Principle. The basic idea is to consider the canonical system in two steps. First we perform a bifurcation analysis of canonical steady states using the continuation and bifurcation package pde2path, yielding a number of so called flat and patterned canonical steady states. In a second step we link pde2path to the two point boundary value problem solver TOM to study time dependent canonical paths to steady states having the so called saddle point property. As an example we consider a shallow lake model with diffusion.