Uniform Conditional Ergodicity and Intrinsic Ultracontractivity

2009 ◽  
Vol 33 (2) ◽  
pp. 107-136 ◽  
Author(s):  
Robert Knobloch ◽  
Lothar Partzsch
Keyword(s):  
Intrinsic Ultracontractivity

scholarly journals Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition

2019 ◽  
Vol 53 (1) ◽  
pp. 57-72
Author(s):  
Marcos Josías Ceballos-Lira ◽  
Aroldo Pérez
Keyword(s):  
Global Existence ◽  
Heat Equation ◽  
Mild Solution ◽  
Blow Up ◽  
Local Existence ◽  
Dirichlet Condition ◽  
Infinite Time ◽  
Diffusion Operator ◽  
Intrinsic Ultracontractivity ◽  
Semilinear Heat Equation

In this paper we prove the local existence of a nonnegative mild solution for a nonautonomous semilinear heat equation with Dirichlet condition, and give sucient conditions for the globality and for the blow up infinite time of the mild solution. Our approach for the global existence goes back to the Weissler's technique and for the nite time blow up we uses the intrinsic ultracontractivity property of the semigroup generated by the diffusion operator.

Sharp estimates for intrinsic ultracontractivity on C 1,α-domains

2007 ◽  
Vol 122 (2) ◽  
pp. 229-244 ◽  
Author(s):  
El Maati Ouhabaz ◽  
Feng-Yu Wang
Keyword(s):  
Intrinsic Ultracontractivity ◽  
Sharp Estimates
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