Existence theorem and global solution for semilinear edge-degenerate hypoelliptic equations



In this article, we use the edge-type of Sobolev inequality,Hardy inequlity and Poincaré inequality to prove the existence theorem for a class of semilinear degenerate hypoelliptic equation on manifolds with conical singularities. In this paper we shall find the existence theorem for the problem 1.1 in cone Sobolev space \({\mathcal {H}}^{1,\frac{N}{2}}_{2,0}({\mathbb {E}}).\) Finally, we obtain existence result of global solutions with exponential decay and show the blow-up in finite time of solutions.


Semilinear equations Edge Sobolev space Totally characteristic degeneracy Global solution Blow-up 

Mathematics Subject Classification

35K10 35B40 58J45 


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© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematical SciencesUniversity of MazandaranBabolsarIran

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