On the Asymptotic Behavior of Solutions of Semilinear Parabolic Equations

1975 ◽  
Vol 28 (1) ◽  
pp. 43-53 ◽  
Author(s):  
J. P. G. Ewer ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behavior ◽  
Parabolic Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Semilinear Parabolic Equations ◽  
Semilinear Parabolic

scholarly journals Semilinear Parabolic Equations on the Heisenberg Group with a Singular Potential

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Houda Mokrani ◽  
Fatimetou Mint Aghrabatt
Keyword(s):  
Asymptotic Behavior ◽  
Heisenberg Group ◽  
Parabolic Equations ◽  
Singular Potential ◽  
Steady States ◽  
Asymptotic Behavior Of Solutions ◽  
Semilinear Parabolic Equations ◽  
Sobolev’S Inequality ◽  
Semilinear Parabolic ◽  
Global Branch

We discuss the asymptotic behavior of solutions for semilinear parabolic equations on the Heisenberg group with a singular potential. The singularity is controlled by Hardy's inequality, and the nonlinearity is controlled by Sobolev's inequality. We also establish the existence of a global branch of the corresponding steady states via the classical Rabinowitz theorem.

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