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Well-posedness of problem with parameter for an integro-differential equation
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AbstractA problem with parameter for an
integro-differential equation is approximated by a
problem with parameter for a loaded differential equation.
The well-posedness of a problem with parameter for the
integro-differential equation is established in the terms of the well-posedness of a problem with parameter for the loaded differential equation. A mutual relationship between the qualitative properties of original
and approximate problems is obtained, and the estimates for
differences between their solutions are set.
A new general solution to the
loaded differential equation with parameter is presented, and its properties are described. The problem with parameter for the loaded differential equation
is reduced to a system of linear algebraic equations
with respect to the arbitrary vectors of a general solution
introduced. The system’s coefficients and right-hand sides are computed
by solving the Cauchy problems for ordinary differential
equations.
Title: Well-posedness of problem with parameter for an integro-differential equation
Description:
AbstractA problem with parameter for an
integro-differential equation is approximated by a
problem with parameter for a loaded differential equation.
The well-posedness of a problem with parameter for the
integro-differential equation is established in the terms of the well-posedness of a problem with parameter for the loaded differential equation.
A mutual relationship between the qualitative properties of original
and approximate problems is obtained, and the estimates for
differences between their solutions are set.
A new general solution to the
loaded differential equation with parameter is presented, and its properties are described.
The problem with parameter for the loaded differential equation
is reduced to a system of linear algebraic equations
with respect to the arbitrary vectors of a general solution
introduced.
The system’s coefficients and right-hand sides are computed
by solving the Cauchy problems for ordinary differential
equations.
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