Multiplicative asymptotics of solutions of the first boundary value problem on a half-axis for a parabolic equation with a small parameter |
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Authors: | Email author" target="_blank">Serguei M?FrolovitchevEmail author |
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Institution: | (1) Department of Applied Mathematics, Moscow Institute of Electronics and Mathematics, MIEM, Bol. Trekhsvyatitelskii 1-3/12, 109028 Moscow, Russia |
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Abstract: | In this work we consider the first boundary value problem for a parabolic equation of second order with a small parameter on a half-axis (i.e., we consider the one-dimensional case). We take the zero initial condition. We construct the global (that is, the caustic points are taken into account) asymptotics of a solution for the boundary value problem. The asymptotic solution of this problem has a different structure depending on the sign of the coefficient (the drift coefficient) at the derivative of first order at a boundary point. The constructed asymptotic solutions are justified. |
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Keywords: | 35B40 35K15 35K20 60J60 |
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