4 papers · 1 filter
Physics-Informed Neural Network for Diffusion-Reaction Problems with Dead-Core Formation in Catalyst Slabs
Piotr Skrzypacz, Kaisar Tangirbergen, Jan Valdman
This work investigates a nonlinear two-point boundary value problem arising in diffusion--reaction processes in catalyst slabs with power-law kinetics and fractional reaction order…
Geometry-induced formation and merging of multiple dead zones in diffusion-reaction problems
Piotr Skrzypacz, Boris Golman, Jan Valdman
This study focuses on dead-core solutions for a two-dimensional isothermal reaction-diffusion problem involving a single chemical reaction described by power-law kinetics within a…
Sharp mean Hadamard inequalities and polyconvex integrands that give rise to convex functionals
Jonathan Bevan, Martin Kružík, Jan Valdman
We investigate several instances of the Hadamard inequality in the mean in two dimensions. As a consequence, we prove the uniqueness of minimizers of an integral functional with a…
Numerical Algorithms for Partially Segregated Elliptic Systems
Farid Bozorgnia, Avetik Arakelyan, Vyacheslav Kungurtsev +1
We develop numerical methods for elliptic systems governed by a ternary partial-segregation constraint, in which three nonnegative components are required to have a vanishing point…