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math.AP2026
Benjamini-Schramm limit of the heat semigroup on quantum graphs
Mihály Kovács, Eszter Sikolya
We study the behaviour of heat semigroups on quantum graphs under Benjamini-Schramm convergence. For quantum graphs with uniformly bounded geometry, equipped with continuity and Ki…
math.AP2020★ 8 cited
On the stochastic Allen-Cahn equation on networks with multiplicative noise
Mihály Kovács, Eszter Sikolya
We consider a system of stochastic Allen-Cahn equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative Gaussian noise driven stochast…
math.AP2012★ 43 cited
Variational and Semigroup Methods for Waves and Diffusion in Networks
Marjeta Kramar Fijavz, Delio Mugnolo, and Eszter Sikolya
We study diffusion and wave equations in networks. Combining semigroup and variational methods we obtain well-posedness and many nice properties of the solutions in general L^p -co…