E-Besov spaces and dissipative equations

Baoxiang Wang

doi:10.3934/cpaa.2004.3.883

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2004, Volume 3, Issue 4: 883-919. Doi: 10.3934/cpaa.2004.3.883

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E-Besov spaces and dissipative equations

Baoxiang Wang^1,

1.
Department of Mathematics, Peking University, Beijing 100871

Received: September 30, 2003

Revised: February 29, 2004

Published: November 2004

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Abstract

The notion of (homogeneous) exponential Besov spaces is introduced and the infinite smoothness of such spaces is shown. Moreover, we consider some applications of exponential Besov spaces to a class of evolution equations involving dissipative terms, such as Cauchy-Riemann equations, semi-linear parabolic equations and semi-linear viscoelastic equations. The existence, uniqueness and regularity of solutions for the Cauchy problem of these equations will be established with rough initial data.

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Mathematics Subject Classification: Primary 46E35, 35K55, 35Q53, 35L75, 47D06.

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