Connecting of local operators and evolution equations on networks

1980 ◽  
pp. 219-234 ◽  
Author(s):  
G. Lumer
Keyword(s):  
Evolution Equations ◽  
Local Operators

scholarly journals Chernoff approximation for semigroups generated by killed Feller processes and Feynman formulae for time-fractional Fokker–Planck–Kolmogorov equations

2018 ◽  
Vol 21 (5) ◽  
pp. 1203-1237 ◽  
Author(s):  
Yana A. Butko
Keyword(s):  
Evolution Equations ◽  
Approximate Solutions ◽  
Dynamics Simulation ◽  
Fractional Evolution Equations ◽  
Fractional Equations ◽  
Dirichlet Type ◽  
Chernoff Theorem ◽  
Local Operators ◽  
Non Local ◽  
Distributed Order

Abstract We consider operator semigroups generated by Feller processes killed upon leaving a given domain. These semigroups correspond to Cauchy–Dirichlet type initial-exterior value problems in this domain for a class of evolution equations with (possibly non-local) operators. The considered semigroups are approximated by means of the Chernoff theorem. For a class of killed Feller processes, the constructed Chernoff approximation leads to a representation of the solution of the corresponding Cauchy–Dirichlet type problem by a Feynman formula, i.e. by a limit of n-fold iterated integrals of certain functions as n → ∞. Feynman formulae can be used for direct calculations, modelling of underlying dynamics, simulation of underlying stochastic processes. Further, a method to approximate solutions of time-fractional evolution equations is suggested. The method is based on connections between time-fractional and time-non-fractional evolution equations as well as on Chernoff approximations for the latter ones. This method leads to Feynman formulae for solutions of time-fractional evolution equations. A class of distributed order time-fractional equations is considered; Feynman formulae for solutions of the corresponding Cauchy and Cauchy–Dirichlet type problems are obtained.

Dichotomy theorems for evolution equations

2008 ◽  
Author(s):  
Alexandru Alin Pogan
Keyword(s):  
Evolution Equations ◽  
Dichotomy Theorems

Local Operators on Banach Modules

2004 ◽  
Vol 104 (2) ◽  
pp. 239-248
Author(s):  
J. Bračič
Keyword(s):  
Banach Modules ◽  
Local Operators

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

Sign in / Sign up

Export Citation Format

Share Document