On the parabolic inverse problem with an unknown source function
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CitationAshyralyev, A., Demirdağ, Ö. ve Erdoğan, A. S. (2009). On the parabolic inverse problem with an unknown source function. Maltepe Üniversitesi. s. 94.
Let Ω be the unit open cube in the n−dimensional Euclidean space R n(0 < xk < 1, 1 ≤ k ≤ n) with boundary S, Ω = Ω ∪ S. In [0, 1] × Ω we consider the mixed boundary value problem for the multidimensional parabolic equation where αr(x) (x ∈ Ω), ϕ(x), ψ(x) (x ∈ Ω) and f(t, x) (t ∈ (0, 1), x ∈ Ω) are given smooth functions and αr(x) ≥ a > 0. The first and second orders of accuracy stable difference schemes for the approximate solution of (1) are presented. Stability, almost coercive stability and coercive stability estimates are obtained. Numerical techniques are developed and algorithms are tested on an example.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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