Global Existence and Blow-Up for a Class of Degenerate Parabolic Systems with Localized Source

作者：Han, Yuzhu; Gao, Wenjie^*

来源：Acta Applicandae Mathematicae, 2010, 112(2): 251-261.

DOI：10.1007/s10440-010-9563-9

• Global existence
• Finite time blow-up
• Localized source
• Degenerate parabolic system
• Global blow-up

This paper deals with a class of localized and degenerate quasilinear parabolic systems u(iota) = f(u) (Delta(u) + a upsilon (x(0),t)), upsilon(iota) = g(upsilon) (Delta upsilon + bu (x(0), t)) with homogeneous Dirichlet boundary conditions. Local existence of positive classical solutions is proven by using the method of regularization. Global existence and blow-up criteria are also obtained. Moreover, the authors prove that under certain conditions, the solutions have global blow-up property.

• 出版日期2010-11
• 单位吉林大学