摘要 :
We extend Balser-Kostov method of studying summability properties of a singularly perturbed inhomogeneous linear system with regular singularity at origin to nonlinear systems of the form εｚｆ′ = Ｆ(ε, ｚ, ｆ) with Ｆ a C~ν-v...
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We extend Balser-Kostov method of studying summability properties of a singularly perturbed inhomogeneous linear system with regular singularity at origin to nonlinear systems of the form εｚｆ′ = Ｆ(ε, ｚ, ｆ) with Ｆ a C~ν-valued function, holomorphic in a polydisc D_ρ ×D_ρ ×D~ν_ρ.We show that its unique formal solution in power series of ε, whose coefficients are holomorphic functions of ｚ, is 1-summable under a Siegel-type condition on the eigenvalues of Ｆ_ｆ(0, 0, 0). The estimates employed resemble the ones used in KAM theorem. A simple lemma is applied to tame convolutions that appear in the power series expansion of nonlinear equations. Applications to spherical Bessel functions and probability theory are indicated.The proposed summability method has certain advantages as it may be applied as well to (singularly perturbed) nonlinear partial differential equations of evolution type.
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A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptotic solution of...
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A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptotic solution of the initial boundary value problems is studied.
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摘要 :
The nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution f...
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The nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied.
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摘要 :
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obta...
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The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
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摘要 :
A class of singularly perturbed boundary value problems for nonlinear equation of the third order with two parameters is considered. Under suitable conditions, using the theory of differential inequalities the existence and asympt...
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A class of singularly perturbed boundary value problems for nonlinear equation of the third order with two parameters is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the solution for boundary value problem are studied.
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A class of nonlinear nonlocal singularly perturbed boundary value problems for elliptic equation with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained,...
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A class of nonlinear nonlocal singularly perturbed boundary value problems for elliptic equation with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series, the boundary layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems is studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed.
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摘要 :
Consider the equation -ε~2Δu_ε + q(x)u_ε = f(u_ε) in R~3, |u(∞)| < ∞, ε = const > 0. Under what assumptions on q(x) and f(u) can one prove that the solution u_ε exists and lim_(ε → 0)u_ε = u(x), where u(x) solves the limiting problem q(...
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Consider the equation -ε~2Δu_ε + q(x)u_ε = f(u_ε) in R~3, |u(∞)| < ∞, ε = const > 0. Under what assumptions on q(x) and f(u) can one prove that the solution u_ε exists and lim_(ε → 0)u_ε = u(x), where u(x) solves the limiting problem q(x)u = f(u)? These are the questions discussed in the paper.
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In this paper, using theory of differential inequalities, the singularly perturbed Robin problems of nonlinear equations εy" = y - ty′ - (y′)~n (t ∈ (-1,1)) are studied. The infection of the boundary values for the asymptotic ...
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In this paper, using theory of differential inequalities, the singularly perturbed Robin problems of nonlinear equations εy" = y - ty′ - (y′)~n (t ∈ (-1,1)) are studied. The infection of the boundary values for the asymptotic behavior of solution is discussed more particularly. The conditions for the existence of asymptotic solutions of the equation with different boundary layers or interior layers are obtained.
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摘要 :
In this paper, using theory of differential inequalities, the singularly perturbed Robin problems of nonlinear equations εy" = y - ty′ - (y′)~n (t ∈ (-1,1)) are studied. The infection of the boundary values for the asymptotic ...
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In this paper, using theory of differential inequalities, the singularly perturbed Robin problems of nonlinear equations εy" = y - ty′ - (y′)~n (t ∈ (-1,1)) are studied. The infection of the boundary values for the asymptotic behavior of solution is discussed more particularly. The conditions for the existence of asymptotic solutions of the equation with different boundary layers or interior layers are obtained.
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摘要 :
A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtaine...
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A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and th expanding theory of power series the initial layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed.
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