Title | Double-sided bounds for solution of one-dimensional heat equation |
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Authors | A. E. Rassadin^{1}^{1}HSE University |

Annotation | In the article, to solve the Cauchy problem on a straight line for a linear diffusion-thermal conductivity equation with initial conditions of a special type, estimates of this solution are obtained from below and from above. Using a numerical test, it is shown that after a certain period of time, any of these estimates can be taken as an approximate solution of this problem. |

Keywords | Poisson integral, direct and reverse H"{o}lder inequalities, error function, compact support, Heaviside step function, relative error |

Citation | Rassadin A. E. ''Double-sided bounds for solution of one-dimensional heat equation'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 198-204. Available at: https://conf.svmo.ru/files/2023/papers/paper32.pdf. - Date of access: 02.12.2023. |

**© SVMO, National Research Mordovia State University, 2023**

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