Bifurcation curves of positive steady-state solutions for a reaction–diffusion problem of lake eutrophication

Yeh, Tzung-Shin

doi:10.1016/j.jmaa.2016.12.063

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…There are many references in studying the bifurcation curveS of (3), cf. [2,10,11,18,12,15,16,21,22]. For instance, Ouyang and Shi [15] obtained the bifurcation diagrams for the problem (3) with nonlinearity f (u) = u p − q q , 1 < p < q.…”

Section: Shao-yuan Huangmentioning

confidence: 99%

Bifurcation diagrams of positive solutions for one-dimensional Minkowski-curvature problem and its applications

Huang¹

2019

Discrete &Amp; Continuous Dynamical Systems - A

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In this paper, we study the classification and evolution of bifurcation curves of positive solutions for one-dimensional Minkowski-curvature problem − u / 1 − u 2 = λf (u), in (−L, L) , u(−L) = u(L) = 0, where λ > 0 is a bifurcation parameter, L > 0 is an evolution parameter, f ∈ C[0, ∞) ∩ C 2 (0, ∞) and there exists β > 0 such that (β − z) f (z) > 0 for z = β. In particular, we find that the bifurcation curve S L is monotone increasing for all L > 0 when f (u)/u is of Logistic type, and is either ⊂-shaped or S-shaped for large L > 0 when f (u)/u is of weak Allee effect type. Finally, we can apply these results to obtain the global bifurcation diagrams in some important applications including ecosystem model.

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Section: Shao-yuan Huangmentioning

confidence: 99%

Bifurcation diagrams of positive solutions for one-dimensional Minkowski-curvature problem and its applications

Huang¹

2019

Discrete &Amp; Continuous Dynamical Systems - A

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“…Although eutrophication has received some attention from the mathematical viewpoint in last decade (see, for instance, the recent publications [19,18,12] and the references therein), the study of artificial circulation as a eutrophication control tool has remained unaddressed in the mathematical literature up to now, as far as we know (we can only mention a recent paper of the authors [15], where a simplified preliminary formulation of the problem is posed and briefly analyzed). Thus, in next section we present a detailed mathematical formulation of the physical problem as a control/state constrained optimal control problem of nonlinear partial differential equations.…”

Section: Introduction: the Environmental Problemmentioning

confidence: 99%

An optimization problem related to water artificial recirculation for controlling eutrophication

Fernández¹,

Martínez²,

Alzarez-Vázquez³

2019

Preprint

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In this work, the artificial recirculation of water is presented and analyzed, from the perspective of the optimal control of partial differential equations, as a tool to prevent eutrophication effects in large waterbodies. A novel formulation of the environmental problem, based on the coupling of nonlinear models for hydrodynamics, water temperature and concentrations of the different species involved in the eutrophication processes, is introduced. After a complete and rigorous analysis of the existence of optimal solutions, a full numerical algorithm for their computation is proposed. Finally, some numerical results for a realistic scenario are shown, in order to prove the efficiency of our approach.

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Inversion Model Design of Chlorophyll a Based on BP Neural Network and Remote Sensing Image

Zhou

Zheng

2020

Lecture Notes in Electrical Engineering

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Bifurcation curves of positive steady-state solutions for a reaction–diffusion problem of lake eutrophication

Cited by 5 publications

References 12 publications

Bifurcation diagrams of positive solutions for one-dimensional Minkowski-curvature problem and its applications

Bifurcation diagrams of positive solutions for one-dimensional Minkowski-curvature problem and its applications

An optimization problem related to water artificial recirculation for controlling eutrophication

Inversion Model Design of Chlorophyll a Based on BP Neural Network and Remote Sensing Image

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