Initial value problems for heat equations generated by strongly elliptic (ρ, Λ)-pseudo-differential operators on Rn

被引：0

作者：

Gao, Yaodong ^{[1
]}

Wong, M. W. ^{[1
]}

机构：

[1] York Univ, Dept Math & Stat, 4700 Keele St, Toronto, ON M3J 1P3, Canada

来源：

JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS | 2022年 / 13卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Pseudo-differential operators; Symbols in S-rho; Lambda(m); L-P-boundedness; (rho; Lambda)-Ellipticity; Strong; Lambda)-ellipticity; Garding's inequality; Poisson's equations; Weak solutions; Strong solutions; Strongly continuous; one-parameter semigroups; Hille-Yosida-Phillips theorem; Initial value problems; Heat equations; Solutions; Mild solutions; HYPOELLIPTIC PSEUDODIFFERENTIAL-OPERATORS;

D O I：

10.1007/s11868-022-00483-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using Garding's inequality for strongly (rho, Lambda)-elliptic pseudo-differential operators on R-n, it is shown that these pseudo-differential operators generate strongly continuous one-parameter semigroups of bounded linear operators on L-2 (R-n). Applications to solutions and mild solutions of initial value problems for heat equations governed by strongly (rho, Lambda)-elliptic pseudo-differential operators on R-n are given.

引用

页数：18

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