Double-sided bounds for solution of one-dimensional heat equation

Title	Double-sided bounds for solution of one-dimensional heat equation
Authors	A. E. Rassadin¹ ¹HSE 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: 21.11.2024.