Positivity and Invariance Properties of Nonisothermal Tubular Reactor Nonlinear Models

Laabissi, Mohamed; Achhab, M.E.; Winkin, Joseph J.; Dochain, Denis

doi:10.1007/978-3-540-44928-7_22

Cited by 6 publications

(12 citation statements)

References 10 publications

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“…In the present work, the chemical reactions are assumed to be isothermal following [13] but we concentrate on the multiplicity of equilibrium states caused by the autocatalyst and higher order of the reaction. It would be interesting to combine the effect of temperature and flow as in [23,37] with our setting here.…”

Section: Introductionmentioning

confidence: 97%

“…The existence of solutions to evolution equation is established, and in certain cases, the multiplicity of the equilibrium profiles is reported (see [23]). In a related work, Dramé [6] proved a more general existence result, and it was showed that the solution is uniformly bounded with a partial description of the limit set.…”

Section: Introductionmentioning

confidence: 99%

“…In [23,37] Winkin et al studied the dynamics of non-isothermal tubular reactors with Arrhenius type kinetics. The existence of solutions to evolution equation is established, and in certain cases, the multiplicity of the equilibrium profiles is reported (see [23]).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exact multiplicity of solutions and S-shaped bifurcation curve for a class of semilinear elliptic equations

Zhao

Wang

Shi

2007

Journal of Mathematical Analysis and Applications

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The set of steady state solutions to a reaction-diffusion equation modeling an autocatalytic chemical reaction is completely determined, when the reactor has spherical geometry, and the spatial dimension is n = 1 or 2 for any reaction order, or n 3 for subcritical reaction order. Bifurcation approach and analysis of linearized problems are used to establish exact multiplicity and precise global bifurcation diagram of positive steady states.

show abstract

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exact multiplicity of solutions and S-shaped bifurcation curve for a class of semilinear elliptic equations

Zhao

Wang

Shi

2007

Journal of Mathematical Analysis and Applications

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“…The positivity (or, more precisely, nonnegativity) property occurs quite frequently in practical applications where the state variables correspond to quantities that do not have real meaning unless they are nonnegative, see e.g. [5,14,15,19,20], for examples of positive infinite dimensional systems that are described by specific partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Positive Stabilization of a Class of Infinite-Dimensional Positive Systems

Achhab

Winkin

2017

Positive Systems

Self Cite

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For a class of positive unstable infinite-dimensional linear systems, a method is described for computing a positively stabilizing state feedback, such that the resulting input trajectory remains in an affine cone. This design results in a possibly negative lower bound on the input, which makes the resulting closed-loop system stable and which maintains the nonnegativity of the state trajectory for specific initial states.

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“…The background of our approach is to be found in [3], [7] and [11]. Other significantly related works are the papers [5], [6], [8] and [12].…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

Equilibrium Profiles for a Class of Tubular Reactor Nonlinear Models

Achhab

Aylaj

Laabissi

Proceedings of the 2005 IEEE International Symposium On, Mediterrean Conference on Control and Automation Intelligent Control,

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The existence of equilibrium profiles for a class of nonlinear systems arising from convection-dispersionreaction processes is investigated. It is reported that there is at least one steady state among the physically feasible states for such models. Our approach is based on nonlinear analysis tools such as dissipativity properties, a subtangential condition, the positivity and the compactness of the related C0-semigroup.

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Positivity and Invariance Properties of Nonisothermal Tubular Reactor Nonlinear Models

Cited by 6 publications

References 10 publications

Exact multiplicity of solutions and S-shaped bifurcation curve for a class of semilinear elliptic equations

Exact multiplicity of solutions and S-shaped bifurcation curve for a class of semilinear elliptic equations

Positive Stabilization of a Class of Infinite-Dimensional Positive Systems

Equilibrium Profiles for a Class of Tubular Reactor Nonlinear Models

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