Blow up in a periodic semilinear heat equation

Fasondini, M.; King, J.R.; Weideman, J.A.C.

doi:10.1016/j.physd.2023.133660

All Outputs (6)

Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport (2023)
Journal Article

Auxin is a well-studied plant hormone, the spatial distribution of which remains incompletely understood. Here, we investigate the effects of cell growth and divisions on the dynamics of auxin patterning, using a combination of mathematical modelling... Read More about Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport.

FUTURE MACHINE: Making Myths & Designing Technology for a Responsible Future: Making Myths and Entanglement: Community engagement at the edge of participatory design and user experience (2023)
Conference Proceeding

This paper explores the unique methods and strategies employed by a team of artists, in collaboration with engineers, programmers, a climate scientist, researchers and members of the public, who have come together to create the Future Machine, with t... Read More about FUTURE MACHINE: Making Myths & Designing Technology for a Responsible Future: Making Myths and Entanglement: Community engagement at the edge of participatory design and user experience.

Electrochemical transport modelling and open-source simulation of pore-scale solid–liquid systems (2023)
Journal Article

The modelling of electrokinetic flows is a critical aspect spanning many industrial applications and research fields. This has introduced great demand in flexible numerical solvers to describe these flows. The underlying phenomena are microscopic, no... Read More about Electrochemical transport modelling and open-source simulation of pore-scale solid–liquid systems.

Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties (2023)
Journal Article
King, J. R., Richardson, G. W., & Foster, J. M. (2023). Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties. European Journal of Applied Mathematics, 34(5), 1099-1132. https://doi.org/10.1017/S0956792523000098

The dynamics of interfaces in slow diffusion equations with strong absorption are studied. Asymptotic methods are used to give descriptions of the behaviour local to a comprehensive range of possible singular events that can occur in any evolution. T... Read More about Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties.

Burgers’ equation in the complex plane (2023)
Journal Article
VandenHeuvel, D. J., Lustri, C. J., King, J. R., Turner, I. W., & McCue, S. W. (2023). Burgers’ equation in the complex plane. Physica D: Nonlinear Phenomena, 448, Article 133686. https://doi.org/10.1016/j.physd.2023.133686

Burgers' equation is a well-studied model in applied mathematics with connections to the Navier-Stokes equations in one spatial direction and traffic flow, for example. Following on from previous work, we analyse solutions to Burgers' equation in the... Read More about Burgers’ equation in the complex plane.

Blow up in a periodic semilinear heat equation (2023)
Journal Article
Fasondini, M., King, J., & Weideman, J. (2023). Blow up in a periodic semilinear heat equation. Physica D: Nonlinear Phenomena, 446, Article 133660. https://doi.org/10.1016/j.physd.2023.133660

Blow up in a one-dimensional semilinear heat equation is studied using a combination of numerical and analytical tools. The focus is on problems periodic in the space variable and starting out from a nearly flat, positive initial condition. Novel res... Read More about Blow up in a periodic semilinear heat equation.