Integral equation solution of the first initial-boundary value problem for the heat equation in domains with non-smooth boundary

1970 ◽  
Vol 23 (5) ◽  
pp. 757-765 ◽  
Author(s):  
Guillermo Miranda
Keyword(s):  
Integral Equation ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Smooth Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Equation Solution ◽  
Initial Boundary Value

scholarly journals An Initial-Boundary Value Problem for a Viscous Compressible Flow

2007 ◽  
Vol 14 (1) ◽  
pp. 123-134
Author(s):  
Friedrich-Karl Hebeker ◽  
George C. Hsiao
Keyword(s):  
Integral Equation ◽  
Boundary Value Problem ◽  
Stokes Equations ◽  
Boundary Value ◽  
Integral Equation Method ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Boundary Integral ◽  
Viscous Compressible Flow ◽  
Initial Boundary Value

Abstract A constructive approach is presented to treat an initial boundary value problem for isothermal Navier–Stokes equations. It is based on a characteristics (Lagrangean) approximation locally in time and a boundary integral equation method via nonstationary potentials. As a basic problem, the latter leads to a Volterra integral equation of first kind which is proved to be uniquely solvable and even coercive in some anisotropic Sobolev spaces. The solution depends continuously upon the data and can be constructed by a quasioptimal Galerkin procedure.

scholarly journals Construction of a solution of a certain evolution equation II

1978 ◽  
Vol 71 ◽  
pp. 181-198 ◽  
Author(s):  
Akinobu Shimizu
Keyword(s):  
Brownian Motion ◽  
Evolution Equation ◽  
Boundary Value Problem ◽  
Bounded Domain ◽  
Smooth Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
One Dimensional ◽  
Initial Boundary Value

Let D be a bounded domain in Rd with smooth boundary ∂D. We denote by Bt, t ≥ 0, a one-dimensional Brownian motion. We shall consider the initial-boundary value problem

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