On the multistep time discretization of linear\newline initial-boundary value problems and their boundary integral equations

1994 ◽  
Vol 67 (3) ◽  
pp. 365-389 ◽  
Author(s):  
Ch. Lubich
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Value ◽  
Time Discretization ◽  
Initial Boundary ◽  
Boundary Integral ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

scholarly journals On a nonclassical problem for the heat equation and the Feller semigroup generated by it

2020 ◽  
Vol 12 (2) ◽  
pp. 297-310
Author(s):  
B.I. Kopytko ◽  
A.F. Novosyadlo
Keyword(s):  
Boundary Integral Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Continuous Functions ◽  
Boundary Integral ◽  
Initial Boundary Value Problems ◽  
Feller Semigroup ◽  
Initial Boundary Value ◽  
Bounded Continuous Functions

The initial boundary value problem for the equation of heat conductivity with the Wenzel conjugation condition is studied. It does not fit into the general theory of parabolic initial boundary value problems and belongs to the class of conditionally correct ones. In space of bounded continuous functions by the method of boundary integral equations its classical solvability under some conditions is established. In addition, it is proved that the obtained solution is a Feller semigroup, which represents some homogeneous generalized diffusion process in the area considered here.

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