arXiv subjects

Putri Zahra Kamalia

Publications and source records attributed to Putri Zahra Kamalia.

3 recordsLinked to original sources

arXiv2021

The principal eigenfunction of the Dirichlet Laplacian with prescribed numbers of critical points on the upper half of a topological torus

We consider the principal eigenvalue problem for the Laplace-Beltrami operator on the upper half of a topological torus under the Dirichlet boundary condition. We present a construction of the upper half of a topological torus that admits the principal eigenfunction having exact numbers of critical points. Furthermore, we manage to identify the locations of all the critical points of the principal eigenfunction explicitly.

math.AP↗

arXiv2020

Patterns with prescribed numbers of critical points on topological tori

We study the existence of critical points of stable stationary solutions to reaction-diffusion problems on topological tori. Stable nonconstant stationary solutions are often called patterns. We construct topological tori and patterns with prescribed numbers of critical points whose locations are explicit.

math.AP↗

arXiv2019

A construction of patterns with many critical points on topological tori

We consider reaction-diffusion equations on closed surfaces in $\mathbb R^3$ having genus $1$. Stable nonconstant stationary solutions are often called patterns. The purpose of this paper is to construct closed surfaces together with patterns having as many critical points as one wants.

math.AP↗