Global and Blow-Up Solutions for a Class of Nonlinear Parabolic Problems under Robin Boundary Condition

Lingling Zhang and Hui Wang

Abstract and Applied Analysis, 2014, vol. 2014, 1-9

Abstract:

We discuss the global and blow-up solutions of the following nonlinear parabolic problems with a gradient term under Robin boundary conditions: , in , , on , , in , where is a bounded domain with smooth boundary . Under some appropriate assumption on the functions , , , , and and initial value , we obtain the sufficient conditions for the existence of a global solution, an upper estimate of the global solution, the sufficient conditions for the existence of a blow-up solution, an upper bound for “blow-up time,†and an upper estimate of “blow-up rate.†Our approach depends heavily on the maximum principles.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:241650

DOI: 10.1155/2014/241650

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