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Well-Posedness of Mild Solutions for Superdiffusion Equations with Spatial Nonlocal Operators.

Authors :
Xi, Xuan-Xuan
Zhou, Yong
Hou, Mimi
Source :
Qualitative Theory of Dynamical Systems; Nov2024, Vol. 23 Issue 5, p1-35, 35p
Publication Year :
2024

Abstract

In this paper, we study the well-posedness for a class of semilinear superdiffusion equations with spatial nonlocal operators. We first establish the Gagliardo–Nirenberg inequality in ψ -Bessel potential spaces. Based on this, the well-posedness results of local and global mild solution for corresponding linear problem are obtained via apriori estimates. We also obtain the well-posedness results for the nonlinear problem under different conditions. These conclusions are mainly based on the Mihlin–Hörmander’s multiplier estimates, embedding theorem and fixed point theory. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
15755460
Volume :
23
Issue :
5
Database :
Complementary Index
Journal :
Qualitative Theory of Dynamical Systems
Publication Type :
Academic Journal
Accession number :
178260535
Full Text :
https://doi.org/10.1007/s12346-024-01084-y