Open Access
Translator Disclaimer
2002 Space-time estimates of linear flow and application to some nonlinear integro-differential equations corresponding to fractional-order time derivative
Hitoshi Hirata, Changxing Miao
Adv. Differential Equations 7(2): 217-236 (2002). DOI: 10.57262/ade/1356651852

Abstract

In this paper we study a class of nonlinear integro-differential equations which correspond to a fractional-order time derivative and interpolate nonlinear heat and wave equations. For this purpose we first establish some space--time estimates of the linear flow which is produced by Mittag--Leffler's functions based on Mihlin--Hörmander's multiplier estimates and other harmonic analysis tools. Using these space--time estimates we prove the well-posedness of a local mild solution of the Cauchy problem for the nonlinear integro-differential equation in $ C([0,T); L^p(\mathbf R^n))$ or $L^q(0, T; L^p(\mathbf R^n))$.

Citation

Download Citation

Hitoshi Hirata. Changxing Miao. "Space-time estimates of linear flow and application to some nonlinear integro-differential equations corresponding to fractional-order time derivative." Adv. Differential Equations 7 (2) 217 - 236, 2002. https://doi.org/10.57262/ade/1356651852

Information

Published: 2002
First available in Project Euclid: 27 December 2012

zbMATH: 1032.45009
MathSciNet: MR1869562
Digital Object Identifier: 10.57262/ade/1356651852

Subjects:
Primary: 35K55
Secondary: 35R10 , 45K05

Rights: Copyright © 2002 Khayyam Publishing, Inc.

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.7 • No. 2 • 2002
Back to Top