On the solvability of some integral equations that arise in the theory of parabolic equations with increasing coefficients
Zabolotko Tetyana Oleksandrivna
1
,
Ivasyshen Stepan Dmytrovych
2
1 Department of Mathematical Physics and Differential Equations, National Technical University of Ukraine "Ihor Sikorsky Kyiv Polytechnic Institute", Kyiv, 03056, Ukraine
2 Department of Mathematical Physics and Differential Equations, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, 01001, Ukraine
Keywords:
integral equations, parabolic equations
Abstract
Integral equations of Volterra-Fredholm type of the second kind with quasi-regular kernels are
considered. Such equations arise in the process of construction and study fundamental solutions
for some parabolic equations with increasing coefficients. Resolvents for these integral equations
are found and estimates of ones are obtained. Estimates are different for the cases of integral
equations according to parabolic equations of the second and arbitrary orders. In the first case the
resolvent is estimated as exponent with constant type of decreasing at infinity. In the second case
the resolvent’s estimate have the form of a series the terms of which contain exponents with types
of decreasing becoming vanishingly small.
Cite
- ACS Style
- Zabolotko, T.O.; Ivasyshen, S.D. On the solvability of some integral equations that arise in the theory of parabolic equations with increasing coefficients. Bukovinian Mathematical Journal. 2016, 2
- AMA Style
- Zabolotko TO, Ivasyshen SD. On the solvability of some integral equations that arise in the theory of parabolic equations with increasing coefficients. Bukovinian Mathematical Journal. 2016; 2(4).
- Chicago/Turabian Style
- Tetyana Oleksandrivna Zabolotko, Stepan Dmytrovych Ivasyshen. 2016. "On the solvability of some integral equations that arise in the theory of parabolic equations with increasing coefficients". Bukovinian Mathematical Journal. 2 no. 4.
Export