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Найденный: 5 Экземпляр 0.001 sn
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Singularly Perturbed Parabolic Problems with Multidimensional Boundary Layers

Asan ÖMÜRALİEV | Meerim İmaş Kızı

The first boundary value problem for a multidimensional parabolic differential equation with a small parameter ε multiplying all derivatives is studied. A complete (i.e., of any order with respect to the parameter) regularized asymptotics of the solution is constructed, which contains a multidimensional boundary layer function that is bounded for x = (x 1, x 2) = 0 and tends to zero as ε → +0 for x ≠ 0. In addition, it contains corner boundary layer functions described by the product of a boundary layer function of the exponential type by a multidimensional parabolic boundary layer function

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Asymptotics of the Solution of a Parabolic Linear System with a Small Parameter

Asan ÖMÜRALİEV

The first boundary value problem is studied for an n-dimensional parabolic linear system of differential equations with a small parameter multiplying the spatial derivative. A complete regularized asymptotics of the solution is constructed for the case in which the system is uniformly Petrovskii parabolic. The asymptotics contains 2n parabolic boundary layer functions described by the complementary error function.

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On a Class of Systems of Linear and Nonlinear Fredholm Integral Equations of the Third Kind with Multipoint Singularities

Avıt ASANOV

Based on a new approach, we show that finding solutions for a class of systems of linear (respectively, nonlinear) Fredholm integral equations of the third kind with multipoint singularities is equivalent to finding solutions of systems of linear (respectively, nonlinear) Fredholm integral equations of the second kind with additional conditions. We study the existence, nonexistence, uniqueness, and nonuniqueness of solutions for this class of systems of Fredholm integral equations of the third kind with multipoint singularities.

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Parabolic Problem with a Power-Law Boundary Layer

Asan ÖMÜRALİEV | Ella ABILAYEVA | Peyil Esengul Kızı

We construct a regularized asymptotics of the solution of the first boundary value problem for a singularly perturbed two-dimensional differential equation of the parabolic type for the case in which the limit equation has a regular singularity. There arise power-law and corner boundary layers along with parabolic ones in such problems.

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One Class of Systems of Linear Fredholm Integral Equations of the Third Kind on the Real Line with Multipoint Singularities

Avıt ASANOV

Using a modification of the approach previously developed by the authors, we show that finding solutions of one class of systems of linear Fredholm integral equations of the third kind on the real line with finitely many multipoint singularities is equivalent to finding solutions of a system of linear Fredholm integral equations of the second kind on the real line with additional conditions imposed on the kernels and the free term. The existence, nonexistence, uniqueness, and nonuniqueness of solutions of systems in this class are studied.

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