On \(x\)-analytic solutions to the Cauchy problem for partial differential equations with retarded variables (Q1915221)
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: On \(x\)-analytic solutions to the Cauchy problem for partial differential equations with retarded variables |
scientific article; zbMATH DE number 889001
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(x\)-analytic solutions to the Cauchy problem for partial differential equations with retarded variables |
scientific article; zbMATH DE number 889001 |
Statements
On \(x\)-analytic solutions to the Cauchy problem for partial differential equations with retarded variables (English)
0 references
20 October 1996
0 references
Summary: We prove some existence results for solutions analytic with respect to the spatial variables to the Cauchy problem for the first-order equation \[ D_t u(t, x)= g(t, x, u(\alpha(t), \beta(t, x)), D_x u(\gamma(t), \delta(t, x))) \] with a dealy and some deviations not only at the function, but also at its derivative. We construct a natural Banach space and a norm which make an adequate integral operator contractive. Due to a useful relation of partial order in this space the main problem is also placed in the theory of monotone iterative techniques.
0 references
Banach contraction principle
0 references
Bielecki's norm
0 references
monotone iterative techniques
0 references
