scholarly journals Mixed Problem for a Parabolic System on a Plane and Boundary Integral Equations

2018 ◽  
Vol 64 (1) ◽  
pp. 20-36
Author(s):  
E A Baderko ◽  
M F Cherepova
Keyword(s):  
Classical Solution ◽  
Integral Equations ◽  
Mixed Problem ◽  
Parabolic System ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Second Order ◽  
Spatial Variable ◽  
One Dimensional ◽  
Smoothness Of Solution

We consider the mixed problem for a one-dimensional (with respect to the spatial variable) second-order parabolic system with Dini-continuous coefficients in a domain with nonsmooth lateral boundaries. Using the method of boundary integral equations, we find a classical solution of this problem. We investigate the smoothness of solution as well.

scholarly journals Classical solution of the mixed problem for a one-dimensional wave equation with second-order derivatives at boundary conditions

2020 ◽  
Vol 55 (4) ◽  
pp. 406-412
Author(s):  
V. I. Korzyuk ◽  
S. N. Naumavets ◽  
V. A. Sevastyuk
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Analytical Form ◽  
Second Order ◽  
Compatibility Conditions ◽  
One Dimensional ◽  
Dimensional Wave

This paper considers the mixed problem for a one-dimensional wave equation with second-order derivatives at boundary conditions. Using the method of characteristics, a classical solution to this problem is found in analytical form. Its uniqueness is proved under the relevant compatibility conditions.

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