scholarly journals On periodic solution of some linear parabolic problem with Bitsadze--Samarskii boundary conditions

2021 ◽  
Author(s):  
Олеся Солонуха
Keyword(s):  
Periodic Solution ◽  
Boundary Conditions ◽  
Parabolic Problem ◽  
Linear Parabolic Problem

scholarly journals Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations

2005 ◽  
Vol 2005 (4) ◽  
pp. 523-536
Author(s):  
Yubin Yan
Keyword(s):  
Difference Method ◽  
Parabolic Equations ◽  
Parabolic Problem ◽  
Approximation Scheme ◽  
Time Derivative ◽  
Nonsmooth Data ◽  
Smoothing Property ◽  
Linear Parabolic Equations ◽  
Linear Parabolic Problem ◽  
Data Error

A smoothing property in multistep backward difference method for a linear parabolic problem in Hilbert space has been proved, where the operator is selfadjoint, positive definite with compact inverse. By using the solutions computed by a multistep backward difference method for the parabolic problem, we introduce an approximation scheme for time derivative. The nonsmooth data error estimate for the approximation of time derivative has been obtained.

scholarly journals Remarks on weak solutions for a nonlocal parabolic problem

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
S. B. de Menezes
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Parabolic Problem ◽  
Galerkin Approximation ◽  
Diffusion Problem ◽  
Fixed Point Result ◽  
Nonlinear Diffusions

We prove a result on existence and uniqueness of weak solutions for a diffusion problem associated with nonlinear diffusions of nonlocal type studied by Chipot and Lovat (1999) by an application of the fixed point result of Schauder. Moreover, making use of Faedo-Galerkin approximation, coupled with some technical ideas, we establish a result on existence of periodic solution.

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