发布求助
文献互助 智能选刊 最新文献

Mathematics in Engineering最新文献

筛选
英文 中文
Global existence for reaction-diffusion evolution equations driven by the $ {text{p}} $-Laplacian on manifolds 流形上$ {text{p}} $-拉普拉斯驱动的反应扩散演化方程的整体存在性
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2022-10-28 DOI: 10.3934/mine.2023070
G. Grillo, Giulia Meglioli, F. Punzo
{"title":"Global existence for reaction-diffusion evolution equations driven by the $ {text{p}} $-Laplacian on manifolds","authors":"G. Grillo, Giulia Meglioli, F. Punzo","doi":"10.3934/mine.2023070","DOIUrl":"https://doi.org/10.3934/mine.2023070","url":null,"abstract":"We consider reaction-diffusion equations driven by the $ p $-Laplacian on noncompact, infinite volume manifolds assumed to support the Sobolev inequality and, in some cases, to have $ L^2 $ spectrum bounded away from zero, the main example we have in mind being the hyperbolic space of any dimension. It is shown that, under appropriate conditions on the parameters involved and smallness conditions on the initial data, global in time solutions exist and suitable smoothing effects, namely explicit bounds on the $ L^infty $ norm of solutions at all positive times, in terms of $ L^q $ norms of the data. The geometric setting discussed here requires significant modifications w.r.t. the Euclidean strategies.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45848351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A symmetry theorem in two-phase heat conductors 两相热导体中的一个对称定理
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2022-10-27 DOI: 10.3934/mine.2023061
Hyeonbae Kang, Shigeru Sakaguchi
{"title":"A symmetry theorem in two-phase heat conductors","authors":"Hyeonbae Kang, Shigeru Sakaguchi","doi":"10.3934/mine.2023061","DOIUrl":"https://doi.org/10.3934/mine.2023061","url":null,"abstract":"We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities, where initially one medium has temperature 0 and the other has temperature 1. Under the assumptions that one medium is bounded and the interface is of class $ C^{2, alpha} $, we show that if the interface is stationary isothermic, then it must be a sphere. The method of moving planes due to Serrin is directly utilized to prove the result.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42417652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Local boundedness for $ p $-Laplacian with degenerate coefficients 退化系数的$p$-Laplacian算子的局部有界性
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2022-09-13 DOI: 10.3934/mine.2023081
P. Bella, Mathias Schaffner
{"title":"Local boundedness for $ p $-Laplacian with degenerate coefficients","authors":"P. Bella, Mathias Schaffner","doi":"10.3934/mine.2023081","DOIUrl":"https://doi.org/10.3934/mine.2023081","url":null,"abstract":"We study local boundedness for subsolutions of nonlinear nonuniformly elliptic equations whose prototype is given by $ nabla cdot (lambda |nabla u|^{p-2}nabla u) = 0 $, where the variable coefficient $ 0leqlambda $ and its inverse $ lambda^{-1} $ are allowed to be unbounded. Assuming certain integrability conditions on $ lambda $ and $ lambda^{-1} $ depending on $ p $ and the dimension, we show local boundedness. Moreover, we provide counterexamples to regularity showing that the integrability conditions are optimal for every $ p > 1 $.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45792059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Potential estimates for fully nonlinear elliptic equations with bounded ingredients 具有有界成分的完全非线性椭圆方程的势估计
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2022-09-05 DOI: 10.3934/mine.2023063
Edgard A. Pimentel, Miguel Walker
{"title":"Potential estimates for fully nonlinear elliptic equations with bounded ingredients","authors":"Edgard A. Pimentel, Miguel Walker","doi":"10.3934/mine.2023063","DOIUrl":"https://doi.org/10.3934/mine.2023063","url":null,"abstract":"<abstract><p>We examine $ L^p $-viscosity solutions to fully nonlinear elliptic equations with bounded-measurable ingredients. By considering $ p_0 < p < d $, we focus on gradient-regularity estimates stemming from nonlinear potentials. We find conditions for local Lipschitz-continuity of the solutions and continuity of the gradient. We survey recent breakthroughs in regularity theory arising from (nonlinear) potential estimates. Our findings follow from – and are inspired by – fundamental facts in the theory of $ L^p $-viscosity solutions, and results in the work of Panagiota Daskalopoulos, Tuomo Kuusi and Giuseppe Mingione <sup>[<xref ref-type=\"bibr\" rid=\"b10\">10</xref>]</sup>.</p></abstract>","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42399113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Uniqueness of entire solutions to quasilinear equations of $ p $-Laplace type p -拉普拉斯型拟线性方程全解的唯一性
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2022-08-28 DOI: 10.3934/mine.2023068
N. Phuc, I. Verbitsky
{"title":"Uniqueness of entire solutions to quasilinear equations of $ p $-Laplace type","authors":"N. Phuc, I. Verbitsky","doi":"10.3934/mine.2023068","DOIUrl":"https://doi.org/10.3934/mine.2023068","url":null,"abstract":"<abstract><p>We prove the uniqueness property for a class of entire solutions to the equation</p>\u0000\u0000<p><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ begin{equation*} left{ begin{array}{ll} -{rm div}, mathcal{A}(x,nabla u) = sigma, quad ugeq 0 quad {text{in }} mathbb{R}^n, {liminflimits_{|x|rightarrow infty}}, u = 0, end{array} right. end{equation*} $end{document} </tex-math></disp-formula></p>\u0000<p>where $ sigma $ is a nonnegative locally finite measure in $ mathbb{R}^n $, absolutely continuous with respect to the $ p $-capacity, and $ {rm div}, mathcal{A}(x, nabla u) $ is the $ mathcal{A} $-Laplace operator, under standard growth and monotonicity assumptions of order $ p $ ($ 1 < p < infty $) on $ mathcal{A}(x, xi) $ ($ x, xi in mathbb{R}^n $); the model case $ mathcal{A}(x, xi) = xi | xi |^{p-2} $ corresponds to the $ p $-Laplace operator $ Delta_p $ on $ mathbb{R}^n $. Our main results establish uniqueness of solutions to a similar problem,</p>\u0000\u0000<p><disp-formula> <label/> <tex-math id=\"FE2\"> begin{document}$ begin{equation*} left{ begin{array}{ll} -{rm div}, mathcal{A}(x,nabla u) = sigma u^q +mu, quad ugeq 0 quad {text{in }} mathbb{R}^n, {liminflimits_{|x|rightarrow infty}}, u = 0, end{array} right. end{equation*} $end{document} </tex-math></disp-formula></p>\u0000<p>in the sub-natural growth case $ 0 < q < p-1 $, where $ mu, sigma $ are nonnegative locally finite measures in $ mathbb{R}^n $, absolutely continuous with respect to the $ p $-capacity, and $ mathcal{A}(x, xi) $ satisfies an additional homogeneity condition, which holds in particular for the $ p $-Laplace operator.</p></abstract>","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48381120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Variational analysis in one and two dimensions of a frustrated spin system: chirality and magnetic anisotropy transitions 受抑自旋系统一维和二维的变分分析：手性和磁各向异性跃迁
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2022-07-18 DOI: 10.3934/mine.2023094
Andrea Kubin, Lorenzo Lamberti
{"title":"Variational analysis in one and two dimensions of a frustrated spin system: chirality and magnetic anisotropy transitions","authors":"Andrea Kubin, Lorenzo Lamberti","doi":"10.3934/mine.2023094","DOIUrl":"https://doi.org/10.3934/mine.2023094","url":null,"abstract":"We study the energy of a ferromagnetic/antiferromagnetic frustrated spin system where the spin takes values on two disjoint circles of the 2-dimensional unit sphere. This analysis will be carried out first on a one-dimensional lattice and then on a two-dimensional lattice. The energy consists of the sum of a term that depends on nearest and next-to-nearest interactions and a penalizing term related to the spins' magnetic anisotropy transitions. We analyze the asymptotic behaviour of the energy, that is when the system is close to the helimagnet/ferromagnet transition point as the number of particles diverges. In the one-dimensional setting we compute the $ Gamma $-limit of scalings of the energy at first and second order. As a result, it is shown how much energy the system spends for any magnetic anistropy transition and chirality transition. In the two-dimensional setting, by computing the $ Gamma $-limit of a scaling of the energy, we study the geometric rigidity of chirality transitions.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47278799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exact solutions for the insulated and perfect conductivity problems with concentric balls 同心球绝缘和完全导电性问题的精确解
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2022-07-12 DOI: 10.3934/mine.2023060
Zhiwen Zhao
{"title":"Exact solutions for the insulated and perfect conductivity problems with concentric balls","authors":"Zhiwen Zhao","doi":"10.3934/mine.2023060","DOIUrl":"https://doi.org/10.3934/mine.2023060","url":null,"abstract":"The insulated and perfect conductivity problems arising from high-contrast composite materials are considered in all dimensions. The solution and its gradient, respectively, represent the electric potential and field. The novelty of this paper lies in finding exact solutions for the insulated and perfect conductivity problems with concentric balls. Our results show that there appears no electric field concentration for the insulated conductivity problem, while the electric field for the perfect conductivity problem exhibits sharp singularity with respect to the small distance between interfacial boundaries of the interior and exterior balls. This discrepancy reveals that concentric balls is the optimal structure of insulated composites, but not for superconducting composites.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42725667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Bloch estimates in non-doubling generalized Orlicz spaces 非二重广义Orlicz空间中的Bloch估计
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2022-07-01 DOI: 10.3934/mine.2023052
Petteri Harjulehto, P. Hasto, Jonne Juusti
{"title":"Bloch estimates in non-doubling generalized Orlicz spaces","authors":"Petteri Harjulehto, P. Hasto, Jonne Juusti","doi":"10.3934/mine.2023052","DOIUrl":"https://doi.org/10.3934/mine.2023052","url":null,"abstract":"<abstract><p>We study minimizers of non-autonomous functionals</p>\u0000\u0000<p><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ begin{align*} inflimits_u int_Omega varphi(x,|nabla u|) , dx end{align*} $end{document} </tex-math></disp-formula></p>\u0000\u0000<p>when $ varphi $ has generalized Orlicz growth. We consider the case where the upper growth rate of $ varphi $ is unbounded and prove the Harnack inequality for minimizers. Our technique is based on \"truncating\" the function $ varphi $ to approximate the minimizer and Harnack estimates with uniform constants via a Bloch estimate for the approximating minimizers.</p></abstract>","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42807804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Kolmogorov algorithm for isochronous Hamiltonian systems 等时哈密顿系统的Kolmogorov算法
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2022-06-20 DOI: 10.3934/mine.2023035
Rita Mastroianni, C. Efthymiopoulos
{"title":"Kolmogorov algorithm for isochronous Hamiltonian systems","authors":"Rita Mastroianni, C. Efthymiopoulos","doi":"10.3934/mine.2023035","DOIUrl":"https://doi.org/10.3934/mine.2023035","url":null,"abstract":"We present a Kolmogorov-like algorithm for the computation of a normal form in the neighborhood of an invariant torus in 'isochronous' Hamiltonian systems, i.e., systems with Hamiltonians of the form $ {mathcal{H}} = {mathcal{H}}_0+varepsilon {mathcal{H}}_1 $ where $ {mathcal{H}}_0 $ is the Hamiltonian of $ N $ linear oscillators, and $ {mathcal{H}}_1 $ is expandable as a polynomial series in the oscillators' canonical variables. This method can be regarded as a normal form analogue of a corresponding Lindstedt method for coupled oscillators. We comment on the possible use of the Lindstedt method itself under two distinct schemes, i.e., one producing series analogous to those of the Birkhoff normal form scheme, and another, analogous to the Kolomogorov normal form scheme in which we fix in advance the frequency of the torus.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42139767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Uniform density estimates and $ Gamma $-convergence for the Alt-Phillips functional of negative powers 负幂的Alt-Phillips泛函的均匀密度估计和$ Gamma $收敛性
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2022-05-17 DOI: 10.3934/mine.2023086
D. Silva, O. Savin
{"title":"Uniform density estimates and $ Gamma $-convergence for the Alt-Phillips functional of negative powers","authors":"D. Silva, O. Savin","doi":"10.3934/mine.2023086","DOIUrl":"https://doi.org/10.3934/mine.2023086","url":null,"abstract":"<abstract><p>We obtain density estimates for the free boundaries of minimizers $ u ge 0 $ of the Alt-Phillips functional involving negative power potentials</p>\u0000\u0000<p><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ int_Omega left(|nabla u|^2 + u^{-gamma} chi_{{u>0}}right) , dx, quad quad gamma in (0, 2). $end{document} </tex-math></disp-formula></p>\u0000\u0000<p>These estimates remain uniform as the parameter $ gamma to 2 $. As a consequence we establish the uniform convergence of the corresponding free boundaries to a minimal surface as $ gamma to 2 $. The results are based on the $ Gamma $-convergence of these energies (properly rescaled) to the Dirichlet-perimeter functional</p>\u0000\u0000<p><disp-formula> <label/> <tex-math id=\"FE2\"> begin{document}$ int_{Omega} |nabla u|^2 dx + Per_{Omega}({ u = 0}), $end{document} </tex-math></disp-formula></p>\u0000\u0000<p>considered by Athanasopoulous, Caffarelli, Kenig, and Salsa.</p></abstract>","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43302985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信