Existence of Solutions to a Class of Doubly Degenerate Equations and Blow up with Vanishing Initial Energy
Received:October 26, 2005  Revised:January 18, 2006
Key Words: doubly degenerate   boundary value problem   blow-up.  
Fund Project:the National Natural Science Foundation of China (10371050)
Author NameAffiliation
WANG Jian Institute of Mathematics, Jilin University, Jilin 130012, China 
GAO Wen-jie Institute of Mathematics, Jilin University, Jilin 130012, China 
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Abstract:
      An initial boundary value problem related to the equation $$u_t-{\rm div}(|\nabla u^m|^{p-2}\nabla u^m)=f(u)$$ is studied in this paper. We prove, under suitable conditions on $f$, a blow up result for solutions with vanishing or negative initial energy. The existence of solutions is also given.
Citation:
DOI:10.3770/j.issn:1000-341X.2007.01.021
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