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January/February 2010 Abstract parabolic equations with applications to problems in cylindrical space domains
Michele Di Cristo, Davide Guidetti, Alfredo Lorenzi
Adv. Differential Equations 15(1/2): 1-42 (January/February 2010).

Abstract

In a Banach space $X$ we consider the partial differential equation $$ (*)\quad D_{t}u(t,x)+(-1)^ma(x)D_{x}^{2m}u(t,x)-A(x)u(t,x)=f(t,x) $$ where $m$ is a positive integer, related to the rectangle $(0,T)\times(0,L)$ and the family of closed linear operators $\{A(x)\}_{x\in[0,L]}$. Under suitable assumptions we uniquely solve certain initial and boundary-value problems associated with $(*)$. Some applications are given when,for each $x,$ $A(x)$ is an explicit linear uniformly elliptic differential operator.

Citation

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Michele Di Cristo. Davide Guidetti. Alfredo Lorenzi. "Abstract parabolic equations with applications to problems in cylindrical space domains." Adv. Differential Equations 15 (1/2) 1 - 42, January/February 2010.

Information

Published: January/February 2010
First available in Project Euclid: 18 December 2012

zbMATH: 1207.35201
MathSciNet: MR2588388

Subjects:
Primary: 34G10, 35K35, 35K70, 47D06

Rights: Copyright © 2010 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.15 • No. 1/2 • January/February 2010
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