10 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…
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…
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 Kružík, Jan Valdman
Let be the Dirichlet energy of a map belonging to the Sobolev space and let be a subclass of whose m…
On semismooth path-following method and uniformity of strong metric subregularity at/around the reference point
Tomáš Roubal, Jan Valdman
This paper investigates a path-following method inspired by the semismooth approach for solving algebraic inclusions, with a primary emphasis on the role of uniform subregulari…
Minimization of Nonlinear Energies in Python Using FEM and Automatic Differentiation Tools
Michal Béreš, Jan Valdman
This contribution examines the capabilities of the Python ecosystem to solve nonlinear energy minimization problems, with a particular focus on transitioning from traditional MATLA…
Hadamard's inequality in the mean
Jonathan Bevan, Martin Kružík, Jan Valdman
Let be a Lipschitz domain in and let . We investigate conditions under which the functional $$I_n(φ)=\int_Q |\nabla φ|^n+ f(x)\,\mathrm{det}…
Verification of functional a posteriori error estimates for obstacle problem in 1D
Petr Harasim, Jan Valdman
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an ex…