6 papers
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…
Numerical simulations for two-dimensional reaction-diffusion problems with formation of multiple dead zones
Piotr Skrzypacz, Boris Golman, Jan Valdman
The paper deals with dead-core solutions to an isothermal reaction-diffusion problem with power-law kinetics for a single reaction that takes place in a chemical reactor represente…
Sharp mean Hadamard inequalities and polyconvex integrands that give rise to convex functionals
Jonathan Bevan, Martin KružÃk, 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 partial segregation constraints, in which three nonnegative components are required to have a vanishing pointwise prod…
On Josephy-Halley method for generalized equations
Tomáš Roubal, Jan Valdman
We extend the classical third-order Halley iteration to the setting of generalized equations of the form \[ 0 \in f(x) + F(x), \] where \(f\colon X\longrightarrow Y\) is twice cont…
New applications of Hadamard-in-the-mean inequalities to incompressible variational problems
Jonathan Bevan, Martin KružÃk, Jan Valdman
Let be the Dirichlet energy of a map belonging to the Sobolev space and let be a subclass of whose…