Summary
We consider the Dirichlet problem for the equation Lε(u) ≡ uxx+ɛuyy++A(x, y)ux−B(y)uy+C(x, y)u=F(x, y) where B(y)>0 and ɛ is a small positive parameter. An asymptotic formula is proved, from which it follows that in a suitable part of the domain of definition u(x, y, ɛ)→U(x, y) as ɛ→0+, where U(x, y) is the solution of the corresponding boundary - value problem for the reduced equation L0(U)≡Uxx+A(x, y)Ux−B(y)U+C(x, y)U=F(x, y).
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To Enrico Bompiani on his scientific Jubilee.
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Zlámal, M. The parabolic equation as a limiting case of a certain elliptic equation. Annali di Matematica 57, 143–150 (1962). https://doi.org/10.1007/BF02417732
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DOI: https://doi.org/10.1007/BF02417732