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April 2022 Well-posedness and parabolic smoothing effect for higher order Schrödinger type equations with constant coefficients
Tomoyuki Tanaka, Kotaro Tsugawa
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Osaka J. Math. 59(2): 465-480 (April 2022).

Abstract

In this paper, we consider the Cauchy problem of a class of higher order Schrödinger type equations with constant coefficients. By employing the energy inequality, we show the $L^2$ well-posedness, the parabolic smoothing and a breakdown of the persistence of regularity. We classify this class of equations into three types on the basis of their smoothing property.

Acknowledgments

The first author was supported by RIKEN Junior Research Associate Program and JSPS KAKENHI Grant Number JP20J12750. The second author was supported by JSPS KAKENHI Grant Number 17K05316.

Citation

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Tomoyuki Tanaka. Kotaro Tsugawa. "Well-posedness and parabolic smoothing effect for higher order Schrödinger type equations with constant coefficients." Osaka J. Math. 59 (2) 465 - 480, April 2022.

Information

Received: 2 November 2020; Revised: 3 March 2021; Published: April 2022
First available in Project Euclid: 7 April 2022

Subjects:
Primary: 35Q55
Secondary: 35A01 , 35B45

Rights: Copyright © 2022 Osaka University and Osaka City University, Departments of Mathematics

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Vol.59 • No. 2 • April 2022
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