Nonlinear Analysis-Real World Applications最新文献

Higher fractional differentiability for solutions to parabolic equations with double-phase growth 双相增长抛物型方程解的高分数可微性

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-11-30 DOI: 10.1016/j.nonrwa.2024.104270

Lijing Zhao, Shenzhou Zheng

引用次数: 0

N-wave-like properties for entropy solutions to scalar parabolic–hyperbolic conservation laws 标量抛物-双曲守恒律熵解的类n波性质

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-11-29 DOI: 10.1016/j.nonrwa.2024.104265

Hiroshi Watanabe

{"title":"N-wave-like properties for entropy solutions to scalar parabolic–hyperbolic conservation laws","authors":"Hiroshi Watanabe","doi":"10.1016/j.nonrwa.2024.104265","DOIUrl":"10.1016/j.nonrwa.2024.104265","url":null,"abstract":"<div><div>In this paper, we consider qualitative properties for entropy solutions to one-dimensional Cauchy problems (CP) for scalar parabolic–hyperbolic conservation laws. Since the equations have both properties of hyperbolic equations and those of parabolic equations, it is difficult to investigate the behavior of solutions to (CP). In our previous works, we focused on the traveling wave structure instead of the self-similar structure. In fact, we succeeded in constructing shock wave type traveling waves with multiple discontinuity. Moreover, we constructed rarefaction wave type sub-, super-solutions to (CP) and investigated their properties.</div><div>In the present paper, we investigate “<span><math><mi>N</mi></math></span>-wave-like properties” for entropy solutions to (CP) while we are not able to construct an analogue of <span><math><mi>N</mi></math></span>-waves. In particular, we derive generalized one-sided Lipschitz estimates (Oleinik type entropy estimates) and decay estimates for entropy solutions to (CP). Based on the decay estimates, we discuss the asymptotic profiles of entropy solutions to (CP) under some specific setting.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104265"},"PeriodicalIF":1.8,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142745191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis of a Navier–Stokes phase-field crystal system 纳维-斯托克斯相场晶体系统分析

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-11-22 DOI: 10.1016/j.nonrwa.2024.104263

Cecilia Cavaterra , Maurizio Grasselli , Muhammed Ali Mehmood , Riccardo Voso

引用次数: 0

Wave breaking for the Degasperis–Procesi equation 德加斯佩里斯-普罗切斯方程的破浪作用

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-11-22 DOI: 10.1016/j.nonrwa.2024.104262

Tiantian Zhao , Kai Yan

引用次数: 0

A novel variable exponent PDE with dependency on γ(u,|∇u0,σ|) for image despeckling application 用于图像消斑的依赖于 γ(u,|∇u0,σ|) 的新型可变指数 PDE

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-11-22 DOI: 10.1016/j.nonrwa.2024.104264

A. Nachaoui , A. Laghrib , A. Hadri , M. Nachaoui

{"title":"A novel variable exponent PDE with dependency on γ(u,|∇u0,σ|) for image despeckling application","authors":"A. Nachaoui , A. Laghrib , A. Hadri , M. Nachaoui","doi":"10.1016/j.nonrwa.2024.104264","DOIUrl":"10.1016/j.nonrwa.2024.104264","url":null,"abstract":"<div><div>Within the realm of image processing, image denoising holds significant importance. This study focuses on tackling denoising challenges posed by Speckle noise. We introduce a novel variable <span><math><mrow><mi>γ</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mrow><mo>|</mo><mo>∇</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn><mo>,</mo><mi>σ</mi></mrow></msub><mo>|</mo></mrow><mo>)</mo></mrow></mrow></math></span>-PDE-based denoising model, offering a fresh perspective. Our approach involves a unique class of PDEs, wherein the nonlinear structure relies on spatially nonlocal exponent dependent factors linked to the target solution and also its gradient. This innovation incorporates grayscale information by introducing the variable exponent <span><math><mi>γ</mi></math></span>, which controls much better the diffusion and incorporates information from wide regions. The existence and uniqueness of the proposed PDE are established through Galerkin’s approximation. Furthermore, a series of experiments are conducted for denoising, including comparisons with other models, in order to validate the selection of the variable exponent parameter. This research contributes to the advancement of image denoising methods with high theoretical foundations and potential implications for other applications.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"83 ","pages":"Article 104264"},"PeriodicalIF":1.8,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Global existence and boundedness of solutions to a two-dimensional forager-exploiter model with/without logistic source 有/无逻辑源的二维觅食者-开发者模型解的全局存在性和有界性

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-11-20 DOI: 10.1016/j.nonrwa.2024.104261

Shengfeng Zhao, Li Xie

引用次数: 0

A class of nonlinear parabolic PDEs with variable growth structure applied to multi-frame MRI super-resolution 一类具有可变增长结构的非线性抛物 PDEs 应用于多帧 MRI 超分辨率

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-11-20 DOI: 10.1016/j.nonrwa.2024.104259

Abderrahim Charkaoui , Anouar Ben-Loghfyry

{"title":"A class of nonlinear parabolic PDEs with variable growth structure applied to multi-frame MRI super-resolution","authors":"Abderrahim Charkaoui , Anouar Ben-Loghfyry","doi":"10.1016/j.nonrwa.2024.104259","DOIUrl":"10.1016/j.nonrwa.2024.104259","url":null,"abstract":"<div><div>This research paper proposes a novel parabolic model driven by a nonlinear operator with a variable exponent applied to multi-frame image super-resolution. Our idea is based essentially on enhancing the classical image super-resolution models by considering novel regularized terms involving <span><math><mrow><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>-growth structure. This regularization leads to deriving a new nonlinear parabolic PDE with nonstandard growth conditions. We start initially by examining the theoretical solvability of our model. We employ the so-called variable exponents Lebesgue-Sobolev spaces to establish an appropriate functional framework for the theoretical investigation of our proposed model. We then apply the <em>Faedo–Galerkin</em> method to establish both the existence and uniqueness of a weak solution for the proposed model. To validate the effectiveness of our model in the multi-frame super resolution (SR) context, we conduct numerical experiments on Magnetic Resonance Images (MRI) featuring diverse characteristics, including corners and edges, while applying different warping, decimation and blurring matrices with noises on the low-resolution (LR) images. We initiate the evaluation by introducing an adaptive discrete scheme of the proposed model. To prove the robustness of our approach, we subject our images to varying levels of noise while conducting many behavior tests on some parameters with major contributions. Additionally, we perform simulations on real data (videos) to show the superiority of the proposed model. The obtained high resolution (HR) results demonstrate notable efficiency and robustness against noise, outperforming the competitive models visually and quantitatively.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"83 ","pages":"Article 104259"},"PeriodicalIF":1.8,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Undercompressive phase transitions for the model of fluid flows in a nozzle with discontinuous cross-sectional area 具有不连续截面积的喷嘴中流体流动模型的欠压缩相变

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-11-16 DOI: 10.1016/j.nonrwa.2024.104260

Duong Xuan Vinh , Mai Duc Thanh , Nguyen Huu Hiep

引用次数: 0

Bifurcation results for a class of elliptic equations with a nonlocal reaction term and interior interface boundary conditions 一类具有非局部反应项和内部界面边界条件的椭圆方程的分岔结果

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-11-16 DOI: 10.1016/j.nonrwa.2024.104258

Braulio B.V. Maia , Alânnio B. Nóbrega

引用次数: 0

Dynamics of an intermittent HIV treatment using piecewise smooth vector fields with two switching manifolds 使用具有两个切换流形的片断平滑矢量场的间歇性艾滋病治疗动力学

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-11-09 DOI: 10.1016/j.nonrwa.2024.104256

Tiago Carvalho , Jackson Cunha , Rodrigo Euzébio , Marco Florentino

{"title":"Dynamics of an intermittent HIV treatment using piecewise smooth vector fields with two switching manifolds","authors":"Tiago Carvalho , Jackson Cunha , Rodrigo Euzébio , Marco Florentino","doi":"10.1016/j.nonrwa.2024.104256","DOIUrl":"10.1016/j.nonrwa.2024.104256","url":null,"abstract":"<div><div>In this paper we study the dynamics of a piecewise smooth vector field modeling an intermittent human immunodeficiency virus treatment where the patient is recurrently submitted and removed from drug administration. In fact, the protocol says that the drugs are administered when the level of CD4<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T defense cells is smaller than a fixed number <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>o</mi><mi>f</mi><mi>f</mi></mrow><mrow><mi>T</mi></mrow></msubsup></math></span>. When the level of CD4<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cells is greater than a fixed number <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>o</mi><mi>n</mi></mrow><mrow><mi>T</mi></mrow></msubsup></math></span> (distinct from <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>o</mi><mi>f</mi><mi>f</mi></mrow><mrow><mi>T</mi></mrow></msubsup></math></span>) the drugs are not administered to provide a better recovery from side effects. Moreover, the orbits of the piecewise smooth vector fields are trapped within a compact set, which proves that the protocol controls the disease.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"82 ","pages":"Article 104256"},"PeriodicalIF":1.8,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0