Some integral properties of the heat equation (Q5948888)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Some integral properties of the heat equation |
scientific article; zbMATH DE number 1672130
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some integral properties of the heat equation |
scientific article; zbMATH DE number 1672130 |
Statements
Some integral properties of the heat equation (English)
0 references
12 November 2001
0 references
difference scheme
0 references
initial boundary value problem
0 references
heat equation
0 references
monotonicity
0 references
0 references
0 references
0 references
The author considers the initial boundary value problem for the heat equation of the form NEWLINE\[NEWLINE\frac{\delta u}{\delta t} = \frac{\delta ^2 u}{\delta x^2},\;x \in (0, 1),\;t>0, \quad u(0, t) = u(1, t) = 0,\;t>0,\;u(x, 0)=u_0 (x),\;x\in [0, 1].\tag{1}NEWLINE\]NEWLINE For the problem (1) a two-parameter difference scheme is constructed. Sufficient conditions that preserve the monotonicity properties of some integrals of the solution on the discrete level with respect to the space and time variables are given.
0 references
