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Sign-Changing Solutions for the One-Dimensional Non-Local sinh-Poisson Equation
Advanced Nonlinear Studies ( IF 1.8 ) Pub Date : 2020-11-01 , DOI: 10.1515/ans-2020-2103
Azahara DelaTorre 1 , Gabriele Mancini 2 , Angela Pistoia 3
Affiliation  

Abstract We study the existence of sign-changing solutions for a non-local version of the sinh-Poisson equation on a bounded one-dimensional interval I, under Dirichlet conditions in the exterior of I. This model is strictly related to the mathematical description of galvanic corrosion phenomena for simple electrochemical systems. By means of the finite-dimensional Lyapunov–Schmidt reduction method, we construct bubbling families of solutions developing an arbitrarily prescribed number sign-alternating peaks. With a careful analysis of the limit profile of the solutions, we also show that the number of nodal regions coincides with the number of blow-up points.

中文翻译:

一维非局部sinh-Poisson方程的变号解

摘要 我们研究了在有界一维区间 I 上,在 I 外部的狄利克雷条件下,sinh-Poisson 方程的非局部版本的符号变化解的存在性。该模型与简单电化学系统的电偶腐蚀现象。通过有限维 Lyapunov-Schmidt 约简方法,我们构建了冒泡系列解决方案,开发出任意规定的数字符号交替峰。通过对解的极限剖面的仔细分析,我们还表明节点区域的数量与爆破点的数量一致。
更新日期:2020-11-01
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