Boundedness of global solutions of nonlocal parabolic equations

1997 ◽  
Vol 30 (2) ◽  
pp. 877-885 ◽  
Author(s):  
Marek Fila
Keyword(s):  
Parabolic Equations ◽  
Global Solutions ◽  
Nonlocal Parabolic Equations

scholarly journals Regularity for solutions of nonlocal parabolic equations II

2014 ◽  
Vol 256 (1) ◽  
pp. 130-156 ◽  
Author(s):  
Héctor Chang-Lara ◽  
Gonzalo Dávila
Keyword(s):  
Parabolic Equations ◽  
Nonlocal Parabolic Equations

Positivity results for a nonlocal elliptic equation

1998 ◽  
Vol 128 (4) ◽  
pp. 697-715 ◽  
Author(s):  
Pedro Freitas ◽  
Guido Sweers
Keyword(s):  
Elliptic Equation ◽  
Eigenvalue Problem ◽  
Parabolic Equations ◽  
Elliptic Systems ◽  
Stationary Solutions ◽  
Second Order ◽  
Real Eigenvalue ◽  
Nonlocal Operator ◽  
Nonlocal Parabolic Equations ◽  
Positive Eigenfunction

In this paper we consider a second-order linear nonlocal elliptic operator on a bounded domain in ℝn (n ≧ 3), and give conditions which ensure that this operator has a positive inverse. This generalises results of Allegretto and Barabanova, where the kernel of the nonlocal operator was taken to be separable. In particular, our results apply to the case where this kernel is the Green's function associated with second-order uniformly elliptic operators, and thus include the case of some linear elliptic systems. We give several other examples. For a specific case which appears when studying the linearisation of nonlocal parabolic equations around stationary solutions, we also consider the associated eigenvalue problem and give conditions which ensure the existence of a positive eigenfunction associated with the smallest real eigenvalue.

scholarly journals Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations

2011 ◽  
Vol 36 (6) ◽  
pp. 1071-1098 ◽  
Author(s):  
Alexander Lorz ◽  
Sepideh Mirrahimi ◽  
Benoît Perthame
Keyword(s):  
Parabolic Equations ◽  
Dirac Mass ◽  
Nonlocal Parabolic Equations
Sign in / Sign up

Export Citation Format

Share Document