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Forward and backward in time Cauchy problems for systems of parabolic‐type PDE with a small parameter
Author(s) -
Danilov V. G.
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400219
Subject(s) - mathematics , operator (biology) , type (biology) , exponential type , cauchy problem , initial value problem , mathematical analysis , class (philosophy) , exponential function , cauchy distribution , parabolic partial differential equation , invariant (physics) , partial differential equation , mathematical physics , ecology , biochemistry , chemistry , repressor , artificial intelligence , biology , computer science , transcription factor , gene
The paper introduces a class of functions where the resolving operator for a system of Kolmogorov–Feller‐type equations with a small parameter is well posed in forward and backward times. The introduced class of functions is invariant under the resolving operator if the solution is understood in the weak sense with an exponential weight. The paper continues the study of [6][V. G. Danilov, ].