Abstract
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.
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Jafari, A.A., Alimohammady, M. Existence theorem and global solution for semilinear edge-degenerate hypoelliptic equations. J. Pseudo-Differ. Oper. Appl. 9, 391–417 (2018). https://doi.org/10.1007/s11868-016-0185-5
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DOI: https://doi.org/10.1007/s11868-016-0185-5