• Corpus ID: 238634720

Reaction-diffusion on a time-dependent interval: refining the notion of 'critical length'

@inproceedings{Allwright2021ReactiondiffusionOA,
  title={Reaction-diffusion on a time-dependent interval: refining the notion of 'critical length'},
  author={Jane Allwright},
  year={2021}
}
A reaction-diffusion equation is studied in a time-dependent interval whose length varies with time. The reaction term is either linear or of KPP type. On a fixed interval, it is well-known that if the length is less than a certain critical value then the solution tends to zero. When the domain length may vary with time, we prove conditions under which the solution does and does not converge to zero in long time. We show that, even with the length always strictly less than the ‘critical length… 

References

SHOWING 1-8 OF 8 REFERENCES
Exact solutions and critical behaviour for a linear growth-diffusion equation on a timedependent domain’, arXiv:2103.11034 (submitted for publication
  • 2021
Spreading and vanishing in nonlinear diffusion problems with free boundaries
We study nonlinear diffusion problems of the form $u_t=u_{xx}+f(u)$ with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free
Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary
TLDR
A spreading-vanishing dichotomy is proved for this diffusive logistic model, namely the species either successfully spreads to all the new environment and stabilizes at a positive equilibrium state, or it fails to establish and dies out in the long run.
Exact solutions and critical behaviour for a linear growth-diffusion equation on a timedependent domain
  • 2021
Erratum: Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary
TLDR
This erratum points out the correct versions of these results in proposals 4.1 and 4.3 of SIAM J. Math.
Spreading speed revisited: Analysis of a free boundary model
TLDR
This work derives the free boundary condition by considering a "population loss" at the spreading front, and corrects some mistakes regarding the range of spreading speed in [11].
Remarks on Sublinear Elliptic Equations’, Nonlinear Analysis, Theory, Methods and Applications
  • 1986