The Cauchy Problem for Shilov Parabolic Equations

V. A. Litovchenko

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The Cauchy Problem for Shilov Parabolic Equations

机译：Shilov抛物线方程的柯西问题

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摘要

We establish well-posed solvability of the Cauchy problem for the Shilov parabolic equations with time-dependent coefficients whose initial data are tempered distributions. For a certain class of equations we state necessary and sufficient conditions for unique solvability of the Cauchy problem whose properties with respect to the spatial variable are typical for a fundamental solution. The results are characterized only by the order and the parabolicity exponent.

机译：我们建立了具有时变系数的Shilov抛物方程的Cauchy问题的适定可解性，其初始数据为回火分布。对于某一类方程式，我们陈述了柯西问题的独特可解性的必要条件和充分条件，其关于空间变量的性质对于基本解来说是典型的。结果仅由阶数和抛物线指数表征。

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来源
《Siberian Mathematical Journal》 |2004年第4期|共11页
作者
V. A. Litovchenko;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Cauchy problem; Shilov parabolicity; S-type space; multiplier;

机译：Cauchy问题;Shilov抛物型;S型空间;乘数;

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The Cauchy Problem for Shilov Parabolic Equations

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