Regularized Asymptotic Solutions of Singularly Perturbed Integral Equations with Two Independent Variables
- 7 Downloads
Lomov’s regularization method is generalized to singularly perturbed integral equations with one-fold and multiple integral operators. We consider the case in which the kernel of the one-fold integral only depends on the time variable and is independent of the spatial variable. In this case, in contrast to Imanaliev’s works, we construct a regularized asymptotic solution of any order (with respect to the parameter). We also study the initialization problem, i.e., the problem of choosing a class of initial data of the problem for which it is possible to pass to the limit in its solution (as the small parameter tends to zero) to some limit operation mode on the whole prescribed set of independent variables, including the boundary layer region.
Unable to display preview. Download preview PDF.
- 3.Lomov, S.A. and Lomov, I.S., Osnovy matematicheskoi teorii pogranichnogo sloya (Foundations of the Mathematical Theory of Boundary Layers), Moscow: Mosk. Gos. Univ., 2011.Google Scholar
- 4.Safonov, V.F. and Bobodzhanov, A.A., Kurs vysshei matematiki. Singulyarno vozmushchennye uravneniya i metod regulyarizatsii (Course of Higher Mathematics. Singularly Perturbed Equations and Regularization Method), Moscow: Izd. Dom MEI, 2012.Google Scholar
- 5.Smirnov, V.I., Kurs vysshei matematiki (Course of Higher Mathematics), Moscow: Gos. Izd. Tekh. Teor. Lit., 1958, Vol. 4.Google Scholar