2019/05/04 by M. V. Dolgopolov, Dolgopolov, M. V., Ирина Николаевна Родионова +2
Mathematics · #32W50 #35S15 #Algebra over a field #Algebraic and Geometric Analysis #Applied mathematics #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Euler equations #Euler's formula #FOS: Mathematics #General Mathematics (math.GM) #Mathematical analysis #Mathematics #Pure mathematics #math.GM #msc:32W50 #msc:35S15
paper · pdf · doi:10.48550/arxiv.1905.01519
3 pages, Preamble to the reports at The STEMM2019 Conference, Uzbek-Israel Scientific Conference Contemporary Problems in Mathematics and Physics (2017) and XI All-Russian Scientific Conference with International Participation Mathematical Modeling and Boundary Value Problems (2019)
arxiv created 2019/05/04 · openalex publication_date 2019/05/04 · arxiv updated 2019/05/07 · openalex created_date 2019/05/09 · openalex updated_date 2026/07/28
We consider the Euler--Darboux equation with parameters modulo 1/2 and generalization to the space 3D analogue. Due to the fact that the Cauchy problem in its classical formulation is incorrect for such parameter values, the authors propose formulations and solutions of modified Cauchy-type problems with parameter values: a) α=β=(1)/(2), b) α=- (1)/(2), β=+ (1)/(2), c) α=β=- (1)/(2). The obtained result is used to formulate an analogue of the Δ1 problem in the first quadrant with the setting of boundary conditions with displacement on the coordinate axes and non-standard conjugation conditions on the singularity line of the coefficients of the equation y=x. The first of these conditions glues the normal derivatives of the desired solution, the~second contains the limit values of the combination of the solution and its normal derivatives. The problem was reduced to a uniquely solvable system of integral equations.