title: ÐÐ°Ð´Ð°ÑÐ° ÐÐ¾ÑÐ¸ Ð´Ð»Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÐÑÐ¹ÐµÑÐ°-ÐÑÑÐ¼Ñ Ð°Ð½ÑÐ»Ð° Ð² Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ðµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Cauchy problem for the Guyer-Krumhansl equation in space
Creators: name: ÐÐ°ÑÑÐ¸Ð½, ÐÐ½Ð´ÑÐµÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: Ð½ÐµÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐµÐ¿Ð»Ð¾Ð¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¾ÑÑÑ
ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÐÑÐ¹ÐµÑÐ°-ÐÑÑÐ¼Ñ Ð°Ð½ÑÐ»Ð°
Ð·Ð°Ð´Ð°ÑÐ° ÐÐ¾ÑÐ¸ Ð² Ð´Ð²ÑÑ - Ð¸ ÑÑÐµÑ Ð¼ÐµÑÐ½Ð¾Ð¼ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ðµ
ÐºÐ°ÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ðµ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ ÑÐµÑÐµÐ½Ð¸Ñ
Ð°ÑÐ¸Ð¼Ð¿ÑÐ¾ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ ÑÐµÑÐµÐ½Ð¸Ñ
non-classical heat conduction
Guyer-Krumhansl equation
Cauchy problem in two and three-dimensional space
qualitative behavior of the solution
asymptotic behavior of the solution

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ ÐÐ¾ÑÐ¸ Ð´Ð»Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÐÑÐ¹ÐµÑÐ°-ÐÑÑÐ¼ÑÐ°Ð½ÑÐ»Ð° Ð² Ð´Ð²ÑÑ- Ð¸ ÑÑÐµÑÐ¼ÐµÑÐ½Ð¾Ð¼ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ðµ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ: 1. ÐÑÐ¸Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ Ð¸ÑÑÐ¾Ð´Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ðº ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÐÑÐ¹ÐµÑÐ°-ÐÑÑÐ¼ÑÐ°Ð½ÑÐ»Ð°, Ð·Ð°Ð²Ð¸ÑÑÑÐµÐ¼Ñ Ð¾Ñ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ. 2. ÐÐ¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐ° Ð·Ð°Ð´Ð°ÑÐ¸ ÐÐ¾ÑÐ¸ Ð´Ð»Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ñ Ð´Ð²ÑÐ¼Ñ Ð²Ð°ÑÐ¸Ð°Ð½ÑÐ°Ð¼Ð¸ Ð½Ð°ÑÐ°Ð»ÑÐ½ÑÑ ÑÑÐ»Ð¾Ð²Ð¸Ð¹. 3. ÐÐ½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸. 4.ÐÐ½Ð°Ð»Ð¸Ð· ÐºÐ°ÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ ÐÐ¾ÑÐ¸ Ñ Ð´ÐµÐ»ÑÑÐ°-ÑÑÐ½ÐºÑÐ¸ÐµÐ¹ Ð² Ð½Ð°ÑÐ°Ð»ÑÐ½ÑÑ ÑÑÐ»Ð¾Ð²Ð¸ÑÑ. 5. ÐÐ½Ð°Ð»Ð¸Ð· Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð°ÑÐ¸Ð¼Ð¿ÑÐ¾ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹. ÐÑÐ»Ð¾ Ð½Ð°Ð¹Ð´ÐµÐ½Ð¾ ÐºÐ°Ðº Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ðµ, ÑÐ°Ðº Ð¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸, Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½ ÑÑÐµÐ±ÑÐµÐ¼ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð·. Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¸ Ð³ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð±ÑÐ»Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐ·ÑÐºÐ° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Python.
description: This work is dedicated to the study of the Cauchy problem for the Guyer-Krumhansl equation in two and three-dimensional space. The tasks that were solved during the work include: 1. Reduction of the original system of equations to the temperature-dependent Guyer-Krumhansl equation. 2. Formulation of the Cauchy problem for the obtained equation with two sets of initial conditions. 3. Analytical and numerical solution of the formulated problem. 4. Analysis of the qualitative behavior of the Cauchy problem solution with a delta function in the initial conditions. 5. Analysis and comparison of the asymptotic behavior of the obtained solutions. Both analytical and numerical solutions of the problem were found, and the required analysis was conducted. Numerical integration and graphical representation of the results were obtained using the Python programming language.