arXiv subjects

Behzad Djafari Rouhani

Publications and source records attributed to Behzad Djafari Rouhani.

4 recordsLinked to original sources

arXiv2026

Limit as $p(x)\rightarrow \infty$ of $p(x)$-Harmonic functions for unbounded $p(x)$

It is shown that if $p_n$ is a sequence of continuous, unbounded exponents on a bounded, smooth domain $Ω\subset {\mathbb R}^n$ with $1<\inf\limits_{x\in Ω}p_n(x)$ and $p_n\rightarrow \infty$ uniformly, then the sequence $(u_n)$ of solutions of the $p_n(\cdot)$-Laplacian converges to the viscosity solution of a suitable differential operator. The novelty here is that each term of the sequence of exponents $(p_n)$ is allowed to be unbounded in $Ω$.

math.AP↗

arXiv2025

$p(x)$-Stability of the Dirichlet problem for Poisson's equation with variable exponents

It is shown that if the sequence $(p_j(x))$ increases uniformly to $p(x)$ in a bounded, smooth domain $Ω$, then the sequence $(u_i)$ of solutions to the Dirichlet problem for the $p_i(x)$-Laplacian with fixed boundary datum $φ$ converges (in a sense to be made precise) to the solution $u_p$ of the Dirichlet problem for the $p(x)$-Laplacian with boundary datum $φ$. A similar result is proved for a decreasing sequence $p_j\searrow p$

math.AP↗

arXiv2023

Impact of resource distributions on the competition of species in stream environment

Our earlier work in \cite{nguyen2022population} shows that concentrating the resources on the upstream end tends to maximize the total biomass in a metapopulation model for a stream species. In this paper, we continue our research direction by further considering a Lotka-Voletrra competition patch model for two stream species. We show that the species whose resource allocations maximize the total biomass has competitive advantage.

q-bio.PE↗

arXiv2023

Maximizing Metapopulation Growth Rate and Biomass in Stream Networks

We consider the logistic metapopulation model over a stream network and use the metapopulation growth rate and the total biomass (of the positive equilibrium) as metrics for different aspects of population persistence. Our objective is to find distributions of resources that maximize these persistence measures. We begin our study by considering stream networks consisting of three nodes and prove that the strategy to maximize the total biomass is to concentrate all the resources in the most upstream locations. In contrast, when the diffusion rates are sufficiently small, the metapopulation growth rate is maximized when all resources are concentrated in one of the most downstream locations. These two main results are generalized to stream networks with any number of patches.

math.DS↗