ABSTRACT
We consider passage to the limit In the sequence of inverse problems https://www.w3.org/1998/Math/MathML"> u t - ∑ i , j = 1 n ∂ ∂ x j [ a i j m ( t , x ) ∂ u ∂ x i ] + ∑ i = 1 n a i m ( t , x ) u x i + + b m ( t , x ) u = f ( t ) g m ( t , x ) + ∑ j = 1 n ∂ h j m ( t , x ) ∂ x j , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062271/3a9a5b62-3a88-4cc5-923a-97624426ebfd/content/math1m.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> u | t = 0 = u 0 m ( x ) , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062271/3a9a5b62-3a88-4cc5-923a-97624426ebfd/content/math2m.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> u | x ϵ ∂ Ω = 0 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062271/3a9a5b62-3a88-4cc5-923a-97624426ebfd/content/math3h.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> ∫ Ω u ( t , x ) w m ( t , x ) d x = φ m ( t ) , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062271/3a9a5b62-3a88-4cc5-923a-97624426ebfd/content/math4m.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> m=1,2,....,∞; here https://www.w3.org/1998/Math/MathML"> ( t , x ) ϵ Q ≡ { ( t , x ) : 0 ≤ t ≤ T , x ∈ Ω ¯ } , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062271/3a9a5b62-3a88-4cc5-923a-97624426ebfd/content/inline-math436.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Ω - is bounded domain In ℝ with smooth boundary.
