On the convergence of the Rothe method in formulating bounded almost-periodic and periodic solutions of a boundary value problem of the parabolic type

1972 ◽  
Vol 15 (3) ◽  
pp. 245-250
Author(s):  
A. P. Mal'tsev
Keyword(s):  
Boundary Value Problem ◽  
Periodic Solutions ◽  
Boundary Value ◽  
Parabolic Type ◽  
Almost Periodic ◽  
Rothe Method

scholarly journals Periodic solutions of the boundary value problem for the nonlinear heat equation

1984 ◽  
Vol 30 (1) ◽  
pp. 99-110 ◽  
Author(s):  
M. N. Nkashama ◽  
M. Willem
Keyword(s):  
Boundary Value Problem ◽  
Heat Equation ◽  
Periodic Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Nonlinear Heat Equation

We prove the existence of generalized periodic solutions of the boundary value problem for the nonlinear heat equation. The proof is based on classical Leray-Schauder's techniques and coincidence degree.

scholarly journals Global theorem of existence and uniqueness of the firstboundary value problem for nonlinear integrodifferential equations ofparabolic type

2017 ◽  
Vol 21 (3) ◽  
pp. 64-72
Author(s):  
O.P. Filatov
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Parabolic Type ◽  
Current Application ◽  
Real Model ◽  
Fuel Tanks ◽  
The Difference ◽  
The Right ◽  
A Current

Global theorem of existence and uniqueness of solution of the first boundary value problem for nonlinear integrodifferential equation of parabolic type is proved. If the right-hand side of the equation is integrally bounded, then we have estimate of the norm of the difference of two solutions, which implies continuous dependence of solution on the initial function and uniqueness of so- lution of the first boundary value problem. The problem under consideration generalizes the real model for measuring the level of incompressible fluid in the fuel tanks missiles. Therefore, such problem have a current application.

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