On a new formulas for a direct and inverse Cauchy problems of heat equation

2013/11/18 by N. N. Yaremko, N. Yaremko, Yaremko, N. +3
Mathematics · #12E10 #65Rxx #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #advanced mathematical theories #math.CA #msc:12E10 #msc:65Rxx

paper · pdf · doi:10.48550/arxiv.1311.4442

9 pages

arxiv created 2013/11/18 · openalex publication_date 2013/11/18 · arxiv updated 2013/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper a solution of the direct Cauchy problems for heat equation is founded in the Hermite polynomial series form. A well-known classical solution of direct problem is represented in the Poisson integral form. The author shows the formulas for the solution of the inverse Cauchy problems have a symmetry with respect to the formulas for the corresponding direct problems. The obtained solution formulas for the inverse problems can serve as a basis for regularizing computational algorithms while well-known classical formula for the solution of inverse problem did not possess such properties and can't be a basis for regularizing computational algorithms.

Related

• Direct and inverse source problems for heat equation in quantum calculus
• On a class of inverse problems for a heat equation with involution\n perturbation
• Inverse problems for q-analogue of the heat equation
• Ordinary differential equations associated with the heat equation
• Direct and Inverse Problems for the Heat Equation with a Dynamic type Boundary Condition