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December  2004, 3(4): 883-919. doi: 10.3934/cpaa.2004.3.883

E-Besov spaces and dissipative equations

Baoxiang Wang 1,

1. 

Department of Mathematics, Peking University, Beijing 100871, China

Received  October 2003 Revised  March 2004 Published  September 2004

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.
Keywords: initial value problem, semi-linear parabolic equation, semi-linear viscoelastic equation, rough initial data, Exponential Besov space, regularity of solutions., Cauchy-Riemann equation.
Mathematics Subject Classification: Primary 46E35, 35K55, 35Q53, 35L75, 47D0.
Citation: Baoxiang Wang. E-Besov spaces and dissipative equations. Communications on Pure & Applied Analysis, 2004, 3 (4) : 883-919. doi: 10.3934/cpaa.2004.3.883
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