On the Cauchy Problem for Integro-Differential Equations in the Scale of Spaces of Generalized Smoothness

Mikulevicius R.; Phonsom C.

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On the Cauchy Problem for Integro-Differential Equations in the Scale of Spaces of Generalized Smoothness

机译：广义平滑空间规模积分微分方程的Cauchy问题

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Parabolic integro-differential model Cauchy problem is considered in the scale of L-p -spaces of functions whose regularity is defined by a scalable Levy measure. Existence and uniqueness of a solution is proved by deriving apriori estimates. Some rough probability density function estimates of the associated Levy process are used as well.

机译：抛物线积分差分模型Cauchy问题是在L-P空间的规模中考虑，其规律性由可扩展的征收度量定义。通过推导Apriori估计证明了解决方案的存在和唯一性。也使用了一些相关征收过程的一些粗略概率密度验证。

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《Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis》 |2019年第3期|共53页
作者
Mikulevicius R.; Phonsom C.;
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作者单位

Univ Southern Calif Los Angeles CA 90007 USA;

Univ Southern Calif Los Angeles CA 90007 USA;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Non-local parabolic integro-differential equations; Levy processes;

机译：非本地抛物线积分微分方程;征收流程;

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专利

1. On the Cauchy Problem for Integro-Differential Equations in the Scale of Spaces of Generalized Smoothness [J] . Mikulevicius R., Phonsom C. Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis . 2019,第3期

机译：广义平滑空间规模积分微分方程的Cauchy问题
2. On Cauchy-Dirichlet Problem in Half-Space for Linear Integro-Differential Equations in Weighted Hoelder Spaces [J] . Mikulevicius Remigijus, Pragarauskas Henrikas Electronic Journal of Probability . 2005,第33期

机译：加权Hoelder空间中线性积分-微分方程的半空间Cauchy-Dirichlet问题。
3. Cauchy problem on fractional integro-differential evolution equations with infinite delay in fractional power space [J] . Jie Xin, JinRong Wang International journal of dynamical systems and differential equations . 2012,第4期

机译：分数次幂空间中具有无限时滞的分数阶积分-微分演化方程的柯西问题
4. Approximate Solution of Singular Integro-Differential Equations by Reduction Methods in Generalized Holder spaces [C] . Feras M. Al-Faqih, Nikos E. Mastorakis, Iurie Caraus WSEAS MATH, TELE-INFO, SIP, CSECS International Conferneces . 2007

机译：广义持有空间中的缩小方法奇异积分微分方程的近似解
5. Some contributions to analysis: A new space of generalized functions for integro-differential equations involving Hilbert transforms, and a note on the non-nuclearity of a space of test functions on Hilbert space. [D] . Donnelly, Roderick Kerry. 1988

机译：对分析的一些贡献：涉及Hilbert变换的积分微分方程的广义函数的新空间，以及关于Hilbert空间上测试函数的空间的非核性的注释。
6. Phase space volume scaling of generalized entropies and anomalous diffusion scaling governed by corresponding non-linear Fokker-Planck equations [O] . Dániel Czégel, Sámuel G. Balogh, Péter Pollner, -1

机译：由相应的非线性Fokker-Planck方程控制的广义熵的相空间体积缩放和反常扩散缩放
7. On the Cauchy problem for integro-differential equations in the scale of spaces of generalized smoothness [O] . Mikulevicius, R., Phonsom, C. 2017

机译：关于积分微分方程的Cauchy问题广义平滑的空间
8. Smooth generalized Newton method for a class of non-smooth equations [R] . Uko, L. 1995

机译：一类非光滑方程的光滑广义牛顿法

On the Cauchy Problem for Integro-Differential Equations in the Scale of Spaces of Generalized Smoothness

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