当前位置:
X-MOL 学术
›
Nonlinearity
›
论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Transition of blow-up mechanisms in k-equivariant harmonic map heat flow
Nonlinearity ( IF 1.7 ) Pub Date : 2020-04-14 , DOI: 10.1088/1361-6544/ab74f4 Paweł Biernat 1 , Yukihiro Seki 2
Nonlinearity ( IF 1.7 ) Pub Date : 2020-04-14 , DOI: 10.1088/1361-6544/ab74f4 Paweł Biernat 1 , Yukihiro Seki 2
Affiliation
In the present article, we consider blow-up phenomena appearing in k-equivariant harmonic map heat flow from to a unit sphere : Here the scalar variable u stands for latitudinal angle on from the north pole to the south pole . The integer corresponds to the eigenvalues associated to eigenmaps , that is, harmonic maps with constant energy density. We prove constructively the existence of asymptotically non-self-similar blow-up solutions with precise description of their local space-time profiles. The blow-up solutions arise from, depending on the combination of d and k, two different approximations of the nonlinear term: either through a Dirac mass supported at the origin or via a Taylor expansion around equator map . Transition of the blow-up mechanisms arises, accordingly.
中文翻译:
k-等变调和图热流中爆破机制的转变
在本文中,我们考虑从单位球体到 k 等变调和图中的热流中出现的爆破现象:这里的标量变量 u 代表从北极到南极的纬度角。整数对应于与 eigenmaps 关联的特征值,即具有恒定能量密度的谐波映射。我们建设性地证明了渐近非自相似爆炸解的存在,并精确描述了它们的局部时空剖面。根据 d 和 k 的组合,爆破解产生于非线性项的两个不同近似值:通过原点支撑的狄拉克质量或通过围绕赤道图的泰勒展开。相应地,出现了爆破机制的转变。
更新日期:2020-04-14
中文翻译:
k-等变调和图热流中爆破机制的转变
在本文中,我们考虑从单位球体到 k 等变调和图中的热流中出现的爆破现象:这里的标量变量 u 代表从北极到南极的纬度角。整数对应于与 eigenmaps 关联的特征值,即具有恒定能量密度的谐波映射。我们建设性地证明了渐近非自相似爆炸解的存在,并精确描述了它们的局部时空剖面。根据 d 和 k 的组合,爆破解产生于非线性项的两个不同近似值:通过原点支撑的狄拉克质量或通过围绕赤道图的泰勒展开。相应地,出现了爆破机制的转变。