Martin’s Problem for Volume-Surface Reaction-Diffusion Systems

  • Jeff MorganEmail author
  • Vandana Sharma
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 47)


We consider a question of global existence for two component volume-surface reaction-diffusion systems. The first of the components diffuses in a region, and then reacts on the boundary with the second component, which diffuses on the boundary. We show that if the first component is bounded a priori on any time interval, and the kinetic terms satisfy a generalized balancing condition, then both solutions exist globally. We also pose an open question in the opposite direction, and give some a priori estimates for associated m component systems.


Reaction-diffusion Volume-surface Systems Global existence A priori estimates 


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Department of Mathematics and StatisticsArizona State UniversityTempeUSA

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