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NUMERICAL ANALYSIS OF A PROBLEM INVOLVING A VISCOELASTIC BODY WITH DOUBLE POROSITY

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Journal of Computational Mathematics 2022年第3期40卷 415-436页

作者： Noelia Bazarra Jose R.Fernandez MariCarme Leseduarte Antonio Magana Ramon Quintanilla Departamento de Matematica Aplicada I Universidade de VigoETSI TelecomunicacionCampus As Lagoas Marcosende s/n36310 VigoSpain departamento de matematicas E.S.E.I.A.A.T.-U.P.C.Colom 1108222 TerrassaBarcelonaSpain

We study from a numerical point of view a multidimensional problem involving a viscoelastic body with two porous structures.The mechanical problem leads to a linear system of three coupled hyperbolic partial differential equations.Its corresponding variational formulation gives rise to three coupled parabolic linear equations.An existence and uniqueness result,and an energy decay property,are recalled.Then,fully discrete approximations are introduced using the finite element method and the implicit Euler scheme.A discrete stability property and a priori error estimates are proved,from which the linear convergence of the algorithm is derived under suitable additional regularity conditions.Finally,some numerical simulations are performed in one and two dimensions to show the accuracy of the approximation and the behaviour of the solution.

关键词： Viscoelasticity with double porosity Finite elements A priori estimates Numerical simulations

Comparison between chikungunya and dengue viruses transmission based on a mathematical model

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International Journal of Biomathematics 2017年第6期10卷 255-276页

作者： Hyun Mo Yang Departamento de Matematica Aplicada Universidade Estadual de Campinas Praca Sergio Buarque de Holanda 651 CEP 13083-859 Campinas Sao Paulo Brazil

Chikungunya and dengue viruses are transmitted by mosquitoes of genus Aedes. Based on a mathematical model dealing with arboviruses transmission that encompasses human and mosquito populations, the risks of dengue and chikungunya infections are compared. By the fact that chikungunya virus attains high viral load earlier than dengue virus in both humans and mosquitoes, the potential risk of chikungunya could be higher than the dengue infection. The risk of arboviruses infections is assessed by the reproduction number R, which is obtained by the next generation matrix method and Routh-Hurwitz criteria.

关键词：登革病毒病毒传播数学模型登革热基孔 Hurwitz 潜在风险病毒感染

Comments on "Non-existence of Shilnikov chaos in continuous-time systems"

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Applied Mathematics and Mechanics(English Edition) 2013年第9期34卷 1175-1176页

作者： A.ALGABA F.FERNANdeZ-SANCHEZ M.MERINO A.J.RODRIGUEZ-LUIS departamento de matematicas Centro de Investigacion de Fisica Teorica y Matematica FIMATUniversity of Huelva Departamento de Matematica Aplicada II E.S.IngenierosUniversity of Sevilla Camino de los Descubrimientos s/n

A paper, ＂Non-existence of Shilnikov chaos in continuous-time systems＂ was published in the journal Applied Mathematics and Mechanics （English Edition）. The authors gave sufficient conditions for the non-existence of homoclinic and heteroclinic orbits in an nth-order autonomous system. Unfortunately, we show in this comment that the proof presented is erroneous and the result is invalid. We also provide two counterexamples of the wrong criterion stated by the authors.

关键词： homoclinic chaos heteroclinic chaos non-existence of Shilnikov chaos

Maschke Type Theorems for Weak Hopf Quasigroups

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Algebra Colloquium 2020年第2期27卷 213-230页

作者： J.N.Alonso Alvarez J.M.Fernández Vilaboa R.González Rodríguez departamento de matematicas Vniversidade de Vigo Campus Universitario Lagoas-MarcosendeE-36280 VigoSpain departamento de matematicas Universidade de Santiago de Compostela E-15771 Santiago de CompostelaSpain Departamento de Matematica Aplicada II Universidade de Vigo Campus Universitario Lagoas-MarcosendeE-36310 VigoSpain

In this paper we give necessary and sufficient conditions for a comodule magma over a weak Hopf quasigroup to have a total integral,thus extending the theories developed in the Hopf algebra,weak Hopf algebra and non-associative Hopf algebra contexts.From this result we also deduce a version of Maschke’s theorems for right(H,B)-Hopf triples associated to a weak Hopf quasigroup H and a right H-comodule magma B.

关键词： (weak)Hopf algebra (weak)Hopf quasigroup integral Maschke theorem

Simultaneous optimization of even flow and land and timber value in forest planning:a continuous approach

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Forest Ecosystems 2021年第4期8卷 645-658页

作者： Jose M.Gonzalez-Gonzalez Miguel E.Vazquez-Mendez Ulises Dieguez-Aranda departamento de Enxenaria Agroforestal Universidade de Santiago de Compostela.Escola Politecnica Superior de EnxenariaR/Benigno Ledo27002 LugoSpain Departamento de Matematica Aplicada Instituto de MatematicasUniversidade de Santiago de Compostela.Escola Politecnica Superior de EnxenariaR/Benigno Ledo27002 LugoSpain

Background:Forest management planning involves deciding which silvicultural treatment should be applied to each stand and at what time to best meet the objectives established for the forest.For this,many mathematical formulations have been proposed,both within the linear and non-linear programming frameworks,in the latter case generally considering integer variables in a combinatorial manner.We present a novel approach for planning the management of forests comprising single-species,even-aged stands,using a continuous,multi-objective formulation(considering economic and even flow)which can be solved with gradient-type methods.Results:The continuous formulation has proved robust in forest with different structures and different number of stands.The results obtained show a clear advantage of the gradient-type methods over heuristics to solve the problems,both in terms of computational time(efficiency)and in the solution obtained(effectiveness).Their improvement increases drastically with the dimension of the problem(number of stands).Conclusions:It is advisable to rigorously analyze the mathematical properties of the objective functions involved in forest management planning models.The continuous bi-objective model proposed in this paper works with smooth enough functions and can be efficiently solved by using gradient-type techniques.The advantages of the new methodology are summarized as:it does not require to set management prescriptions in advance,it avoids the division of the planning horizon into periods,and it provides better solutions than the traditional combinatorial formulations.Additionally,the graphical display of trade-off information allows an a posteriori articulation of preferences in an intuitive way,therefore being a very interesting tool for the decision-making process in forest planning.

关键词： Even-aged forest management Forest-level optimization Continuous optimization Gradient-type algorithms

COMPLEXITY OF LARGE TIME BEHAVIOUR OF EVOLUTION EQUATIONS WITH BOUNdeD DATA

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Chinese Annals of Mathematics,Series B 2002年第2期23卷 293-310页

作者： J.L.VZQUEZ E.ZUAZUA departamento de matematicas Universidad AutonomaDepartamento de Matematica AplicadaUniversidadComplutense 28049MadridSpain28040 M

The authors study the asymptotic behaviour of solutions of the heat equation and a number of evolution equations using scaling techniques. It is proved that in the framework of bounded data stabilization need not occur and the general asymptotic behaviour is complex. This behaviour reflects for large times, even on compact sets, the complexity of the initial data at infinity.

关键词：复杂性大时间行为发展方程有界数据热方程 Omega极限双曲守恒定律半群收敛性

A Characterization of Semilinear Surjective Operators and Applications to Control Problems

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Applied Mathematics 2010年第4期1卷 265-273页

作者： Edgar Iturriaga Hugo Leiva Grupo de matematica aplicada Departamento de Matematicas Universidad de Los Andes

In this paper we characterize a broad class of semilinear surjective operators given by the following formula where Z are Hilbert spaces, and is a suitable nonlinear function. First, we give a necessary and sufficient condition for the linear operator to be surjective. Second, we prove the following statement: If and is a Lipschitz function with a Lipschitz constant small enough, then and for all the equation admits the following solution .We use these results to prove the exact controllability of the following semilinear evolution equation , , where , are Hilbert spaces, is the infinitesimal generator of strongly continuous semigroup in the control function belong to and is a suitable function. As a particular case we consider the semilinear damped wave equation, the model of vibrating plate equation, the integrodifferential wave equation with delay, etc.

关键词： Semilinear Surjective Operators Evolution Equations Controllability Damped Wave Equation

A Diffusively Corrected Multiclass Lighthill-Whitham-Richards Traffic Model with Anticipation Lengths and Reaction Times

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Advances in Applied Mathematics and Mechanics 2013年第5期5卷 728-758页

作者： Raimund Burger Pep Mulet Luis M.Villada CI2MA and departamento de Ingenierıa matematica Facultad de Ciencias Fısicas y MatematicasUniversidad de ConcepcionCasilla 160-CConcepcionChile departament de matematica aplicada Universitat de ValenciaAv.Dr.Moliner 50E-46100 BurjassotSpain

Multiclass Lighthill-Whitham-Richards trafficmodels[Benzoni-Gavage and Colombo,Euro.J.Appl.Math.,14(2003),pp.587–612;Wong and Wong,Transp.Res.A,36(2002),pp.827–841]give rise to first-order systems of conservation laws that are hyperbolic under usual conditions,so that their associated Cauchy problems are wellposed.Anticipation lengths and reaction times can be incorporated into these models by adding certain conservative second-order terms to these first-order conservation laws.These terms can be diffusive under certain circumstances,thus,in principle,ensuring the stability of the solutions.The purpose of this paper is to analyze the stability of these diffusively correctedmodels under varying reaction times and anticipation lengths.It is demonstrated that instabilities may develop for high reaction times and short anticipation lengths,and that these instabilities may have controlled frequencies and amplitudes due to their nonlinear nature.

关键词： Traffic flow multispecies model anticipation length reaction time diffusive correction quasilinear system of second-order Pdes stability numerical simulation

A Comparison of Semi-Lagrangian and Lagrange-Galerkin hp-FEM Methods in Convection-Diffusion Problems

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Communications in Computational Physics 2011年第4期9卷 1020-1039页

作者： Pedro Galan del Sastre Rodolfo Bermejo Departamento de Matematica Aplicada al Urbanismo a la Edificacion y al Medio AmbienteE.T.S.A.M.Universidad Politecnica de MadridAvda.Juan de Herrera 428040 MadridSpain Departamento de Matematica Aplicada E.T.S.I.I.Universidad Politecnica de MadridC/Jose Gutierrez Abascal 228006 MadridSpain

We perform a comparison in terms of accuracy and CPU time between second order BDF semi-Lagrangian and Lagrange-Galerkin schemes in combination with high order finite element method.The numerical results show that for polynomials of degree 2 semi-Lagrangian schemes are faster than Lagrange-Galerkin schemes for the same number of degrees of freedom,however,for the same level of accuracy both methods are about the same in terms of CPU time.For polynomials of degree larger than 2,Lagrange-Galerkin schemes behave better than semi-Lagrangian schemes in terms of both accuracy and CPU time;specially,for polynomials of degree 8 or larger.Also,we have performed tests on the parallelization of these schemes and the speedup obtained is quasi-optimal even with more than 100 processors.

关键词： Navier-Stokes equations convection-diffusion equations semi-Lagrangian LagrangeGalerkin second order backward difference formula hp-finite element method