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AbstractA singularly perturbed parabolic equation $${\varepsilon ^2}\left( {{{\text{a}}^2}\frac{{{\partial ^2}u}}{{\partial {x^2}}} - \frac{{\partial u}}{{\partial t}}} \right) = F\left( {u,x,t,\varepsilon } \right)$$ε2(a2∂2u∂x2−∂u∂t)=F(u,x,t,ε) is considered in a rectangle with boundary conditions of the… Click to show full abstract
AbstractA singularly perturbed parabolic equation $${\varepsilon ^2}\left( {{{\text{a}}^2}\frac{{{\partial ^2}u}}{{\partial {x^2}}} - \frac{{\partial u}}{{\partial t}}} \right) = F\left( {u,x,t,\varepsilon } \right)$$ε2(a2∂2u∂x2−∂u∂t)=F(u,x,t,ε) is considered in a rectangle with boundary conditions of the first kind. The function F at the corner points of the rectangle is assumed to be monotonic with respect to the variable u on the interval from the root of the degenerate equation to the boundary condition. A complete asymptotic expansion of the solution as ε → 0 is constructed, and its uniformity in the closed rectangle is proven.
Journal Title: Computational Mathematics and Mathematical Physics
Year Published: 2018
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