M. Ammi, Ibrahim Dahi, A. E. Hachimi, Delfim F. M. Torres
{"title":"Existence result of the global attractor for a triply nonlinear thermistor problem","authors":"M. Ammi, Ibrahim Dahi, A. E. Hachimi, Delfim F. M. Torres","doi":"10.2478/mjpaa-2023-0002","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0002","url":null,"abstract":"Abstract We study the existence and uniqueness of a bounded weak solution for a triply nonlinear thermistor problem in Sobolev spaces. Furthermore, we prove the existence of an absorbing set and, consequently, the universal attractor.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"27 - 47"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44177797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Nonlocal Model for Reconstructing Images Corrupted by Cauchy Noise","authors":"F. Bendaida","doi":"10.2478/mjpaa-2023-0003","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0003","url":null,"abstract":"Abstract The aim of this paper is to present the mathematical and numerical study of a nonlocal nonlinear model based on the variable exponent p(x)-Laplacian for removing Cauchy noise, which is a type of impulsive and non-Gaussian degradation. The proposed model benefits from the performance of the nonlocal approach to preserve small details and textures, and the efficiency of the variable exponent to reduce the execution time. To demonstrate the reliability of our proposed model, we provide some experimental denoising results and illustrate the comparison with some models from the literature.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"48 - 64"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48424936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Numerical comparison of three a posteriori error estimators for nonconforming finite element method","authors":"B. Achchab, A. Agouzal, K. Bouihat, A. Majdoubi","doi":"10.2478/mjpaa-2023-0001","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0001","url":null,"abstract":"Abstract In this paper, we propose to compare three a posteriori error estimators namely equilibrated, star-based and residual based for the Poisson problem and the Stokes problem with lowest-order Crouzeix-Raviart finite element discretization. The numerical results are presented to compare the performance of the three estimators in an adaptive refinement strategy.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"1 - 26"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46939497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fractional optimal control problem for a mathematical modeling of African swine fever virus transmission","authors":"A. Kouidere, O. Balatif, M. Rachik","doi":"10.2478/mjpaa-2023-0007","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0007","url":null,"abstract":"Abstract To have a more realistic model, in this paper, This manuscript is devoted to investigating a fractional-order mathematical model of Kouidere et al. That describes the dynamics of spread of African swine fever virus (ASFV). The aim of this work is to protect susceptible pigs from the virus, In our model, by including three controls which represent: the iron fencing and spraying pesticides and get rid. The aims of this paper is to reduce the number of infected pigs and ticks by using optimal control strategy and fractinal order derivation. Pontryagin’s maximal principle is used to describe optimal controls with Caputo time-fractional derivative and the optimal system is resolved in an iterative manner. Numerical simulations are presented based on the presented method. We finished tis article with a conclusion.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"97 - 110"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69233473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"About the valuation of American option under Black-Scholes model : a numerical study","authors":"R. Malek","doi":"10.2478/mjpaa-2023-0005","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0005","url":null,"abstract":"Abstract In the history of option pricing, Black-Scholes model is one of the most significant models. In this paper, we present a new numerical strategy for valuing American option pricing problems governed by Black-Scholes model (BSM). Numerical computations are carried out to show the efficiency and robustness of the proposed method. We compare our numerical solution with the ones based on Finite Element Method (FEM) and the Enriched Finite Element Method (PUFEM). Our result shows the efficiency of the proposed strategy. In addition, that approach can be used to treat nonlinear evolutionary problems.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"75 - 85"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42774876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Existence of solutions for 4p-order PDES with Neumann boundary conditions","authors":"N. Moradi, F. Moradi, S. E. Habib, M. Addam","doi":"10.2478/mjpaa-2023-0004","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0004","url":null,"abstract":"Abstract In this work, we study the existence of at least one non decreasing sequence of nonnegative eigenvalues for the problem: { Δ2pu=λm(x)u in Ω,∂u∂v=∂(Δu)∂v=…=∂(Δ2p-1u)∂v=0 on ∂Ω. left{ {matrix{ {{Delta ^{2p}}u = lambda mleft( x right)u,,,in,,,Omega ,} cr {{{partial u} over {partial v}} = {{partial left( {Delta u} right)} over {partial v}} = ldots = {{partial left( {{Delta ^{2p - 1}}u} right)} over {partial v}} = 0,,,on,,,partial Omega .} cr } } right. Where Ω is a bounded domain in ℝN with smooth boundary ∂ Ω, p ∈ ℕ*, m ∈ L∞ (Ω), and Δ2pu := Δ (Δ...( Δu)), 2p times the operator Δ.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"65 - 74"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44640896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ahmed Nafidi, Ilyasse Makroz, B. Achchab, R. Gutiérrez-Sánchez
{"title":"Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application","authors":"Ahmed Nafidi, Ilyasse Makroz, B. Achchab, R. Gutiérrez-Sánchez","doi":"10.2478/mjpaa-2023-0009","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0009","url":null,"abstract":"Abstract We propose a novel diffusion process having a mean function equal to the Pareto probability density function up to a constant of proportionality. We examine the probabilistic properties of the proposed model. Then, referring to the problem of statistical inference, we describe the approach employed to tackle the issue of obtaining parameter estimates by maximizing the likelihood function based on discrete sampling. This estimation reduces to solving a set of complex equations, that is accomplished using the simulated annealing algorithm. A simulation study is also given to validate the methodology presented. Finally, using a real-world example of the Moroccan child mortality rate, we obtain the fits and forecasts by employing the suggested stochastic process and nonlinear regression model.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"127 - 140"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44975151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Cyclicity in de Branges–Rovnyak spaces","authors":"E. Fricain, S. Grivaux","doi":"10.2478/mjpaa-2023-0016","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0016","url":null,"abstract":"Abstract In this paper, we study the cyclicity problem with respect to the forward shift operator Sb acting on the de Branges–Rovnyak space ℋ (b) associated to a function b in the closed unit ball of H∞ and satisfying log(1− |b| ∈ L1(𝕋). We present a characterisation of cyclic vectors for Sb when b is a rational function which is not a finite Blaschke product. This characterisation can be derived from the description, given in [22], of invariant subspaces of Sb in this case, but we provide here an elementary proof. We also study the situation where b has the form b = (1+ I)/2, where I is a non-constant inner function such that the associated model space KI = ℋ (I) has an orthonormal basis of reproducing kernels.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"216 - 237"},"PeriodicalIF":0.0,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46379369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Limit points for descent spectrum of operator matrices","authors":"H. Boua, M. Karmouni, A. Tajmouati","doi":"10.2478/mjpaa-2022-0024","DOIUrl":"https://doi.org/10.2478/mjpaa-2022-0024","url":null,"abstract":"Abstract In this paper, we investigate the limit points set of descent spectrum of upper triangular operator matrices MC=(AC0B) {M_C} = left( {matrix{A hfill & C hfill cr 0 hfill & B hfill cr } } right) . We prove that acc(σdes(MC)) ∪ Waccσdes = acc(σdes(A)) ∪ acc(σdes(B)) where Waccσdes is the union of certain holes in acc(σdes(MC)), which happen to be subsets of acc(σasc(B)) ∩ acc(σdes(A)). Furthermore, several sufficient conditions for acc(σdes(MC)) = acc(σdes(A)) ∪ acc(σdes(B)) holds for every C ∈ ℬ(Y, X) are given.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"8 1","pages":"358 - 363"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47523801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Existence and Regularity for Solution to a Degenerate Problem with Singular Gradient Lower Order Term","authors":"H. Khelifi","doi":"10.2478/mjpaa-2022-0022","DOIUrl":"https://doi.org/10.2478/mjpaa-2022-0022","url":null,"abstract":"Abstract We study the existence and regularity results for non-linear elliptic equation with degenerate coercivity and a singular gradient lower order term. The model problems is { -div(b(x)| ∇u |p-2∇u(1+| u |)γ)+| ∇u |p| u |θ=f,in Ω,u=0,on ∂Ω, left{ {matrix{ { - divleft( {bleft( x right){{{{left| {nabla u} right|}^{p - 2}}nabla u} over {left( {1 + left| u right|} right)gamma }}} right) + {{{{left| {nabla u} right|}^p}} over {{{left| u right|}^theta }}} = f,} hfill & {in,Omega ,} hfill cr {u = 0,} hfill & {on,partial Omega ,} hfill cr } } right. swhere Ω is a bounded open subset in ℝN, 1 ≤ θ < 2, p > 2 and γ > 0. We will show that, even if the lower order term is singular, we obtain existence and regularity of positive solution, under various assumptions on the summability of the source f.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"8 1","pages":"310 - 327"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47857091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}