Nonlinear Differential Equations and Applications (NoDEA)最新文献_第4页

Heteroclinic solutions for some classes of prescribed mean curvature equations in whole $$mathbb {R}^2$$ 整$$mathbb {R}^2$$ 中几类规定平均曲率方程的异次元解

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-06-06 DOI: 10.1007/s00030-024-00965-0

Claudianor O. Alves, Renan J. S. Isneri

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Wigner analysis of fourier integral operators with symbols in the Shubin classes 具有舒宾类符号的傅里叶积分算子的维格纳分析

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-06-04 DOI: 10.1007/s00030-024-00961-4

Elena Cordero, Gianluca Giacchi, Luigi Rodino, Mario Valenzano

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Properties of set-valued Young integrals and Young differential inclusions generated by sets of Hölder functions 由霍尔德函数集生成的集值杨积分和杨微分夹杂的性质

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-06-04 DOI: 10.1007/s00030-024-00963-2

Mariusz Michta, Jerzy Motyl

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Decay of the radius of spatial analyticity for the modified KdV equation and the nonlinear Schrödinger equation with third order dispersion 修正 KdV 方程和三阶分散非线性薛定谔方程空间解析性半径的衰减

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-05-31 DOI: 10.1007/s00030-024-00960-5

Renata O. Figueira, Mahendra Panthee

{"title":"Decay of the radius of spatial analyticity for the modified KdV equation and the nonlinear Schrödinger equation with third order dispersion","authors":"Renata O. Figueira, Mahendra Panthee","doi":"10.1007/s00030-024-00960-5","DOIUrl":"https://doi.org/10.1007/s00030-024-00960-5","url":null,"abstract":"We consider the initial value problems (IVPs) for the modified Korteweg–de Vries (mKdV) equation $$begin{aligned} left{ begin{array}{l} partial _t u+ partial _x^3u+mu u^2partial _xu =0, quad xin mathbb {R},; tin mathbb {R}, u(x,0) = u_0(x), end{array}right. end{aligned}$$where u is a real valued function and (mu =pm 1), and the cubic nonlinear Schrödinger equation with third order dispersion (tNLS equation in short) $$begin{aligned} left{ begin{array}{l} partial _t v+ialpha partial _x^2v+beta partial _x^3v+igamma |v|^2v = 0, quad xin mathbb {R},; tin mathbb {R}, v(x,0) = v_0(x), end{array}right. end{aligned}$$where (alpha , beta ) and (gamma ) are real constants and v is a complex valued function. In both problems, the initial data (u_0) and (v_0) are analytic on (mathbb {R}) and have uniform radius of analyticity (sigma _0) in the space variable. We prove that the both IVPs are locally well-posed for such data by establishing an analytic version of the trilinear estimates, and showed that the radius of spatial analyticity of the solution remains the same (sigma _0) till some lifespan (0<T_0le 1). We also consider the evolution of the radius of spatial analyticity (sigma (t)) when the local solution extends globally in time and prove that for any time (Tge T_0) it is bounded from below by (c T^{-frac{4}{3}}), for the mKdV equation in the defocusing case ((mu = -1)) and by (c T^{-(4+varepsilon )}), (varepsilon >0), for the tNLS equation. The result for the mKdV equation improves the one obtained in Bona et al. (Ann Inst Henri Poincaré 22:783–797, 2005) and, as far as we know, the result for the tNLS equation is the new one.","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141187758","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}

引用次数: 0

Life-span of solutions for a nonlinear parabolic system 非线性抛物线系统解的寿命期

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-05-28 DOI: 10.1007/s00030-024-00952-5

Slim Tayachi

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Scalar conservation law in a bounded domain with strong source at boundary 边界强源有界域中的标量守恒定律

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-05-25 DOI: 10.1007/s00030-024-00959-y

Lu Xu

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Unique ergodicity in stochastic electroconvection 随机电对流中的独特遍历性

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-05-15 DOI: 10.1007/s00030-024-00954-3

Elie Abdo, Nathan Glatt-Holtz, Mihaela Ignatova

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Homogenization of quasilinear problems with semilinear terms and Signorini boundary conditions in perforated domains 穿孔域中带有半线性项和 Signorini 边界条件的准线性问题的均质化

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-05-11 DOI: 10.1007/s00030-024-00957-0

Jake Avila

引用次数: 0

Variational theory for the resonant T-curvature equation 共振 T 型曲率方程的变量理论

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-05-11 DOI: 10.1007/s00030-024-00953-4

Cheikh Birahim Ndiaye

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Convergence problem of the generalized Kadomtsev–Petviashvili II equation in anisotropic Sobolev space 各向异性索波列夫空间中广义卡多姆采夫-彼得维亚什维利 II方程的收敛问题

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-05-09 DOI: 10.1007/s00030-024-00949-0

Qiaoqiao Zhang, Meihua Yang, Haoyuan Xu, Wei Yan

{"title":"Convergence problem of the generalized Kadomtsev–Petviashvili II equation in anisotropic Sobolev space","authors":"Qiaoqiao Zhang, Meihua Yang, Haoyuan Xu, Wei Yan","doi":"10.1007/s00030-024-00949-0","DOIUrl":"https://doi.org/10.1007/s00030-024-00949-0","url":null,"abstract":"The almost everywhere pointwise and uniform convergences for the generalized KP-II equation are investigated when the initial data is in anisotropic Sobolev space (H^{s_{1},s_{2}}({textbf{R}}^{2})). Firstly, we show that the solution u(x, y, t) converges pointwisely to the initial data (f(x, y)in H^{s_{1},s_{2}}({{textbf{R}}}^{2}) ) for a.e. ((x, y) in {textbf{R}}^{2}) when (s_{1}ge frac{1}{4}), (s_{2}ge frac{1}{4}). The proof relies upon the Strichartz estimate and high-low frequency decomposition. Secondly, We prove that (s_{1}ge frac{1}{4}), (s_{2}ge frac{1}{4}) is a necessary condition for the maximal function estimate of the generalized KP-II equation to hold. Finally, by using the Fourier restriction norm method, we establish the nonlinear smoothing estimate to show the uniform convergence of the generalized KP-II equation in (H^{s_{1},s_{2}} ({{textbf{R}}}^{2}) ) with ( s_{1}ge frac{3}{2}-frac{alpha }{4}+epsilon , s_{2}>frac{1}{2}) and (alpha ge 4 ).\u0000","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"156 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931075","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}

引用次数: 0