The Maximal Regularity of Nonlinear Second-Order Hyperbolic Boundary Differential Equations
In this paper, we show the maximal regularity of nonlinear second-order hyperbolic boundary differential equations. We aim to show if the given second-order partial differential operator satisfies the specific ellipticity condition; additionally, if solutions of the function, which are related to th...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/13/12/884 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this paper, we show the maximal regularity of nonlinear second-order hyperbolic boundary differential equations. We aim to show if the given second-order partial differential operator satisfies the specific ellipticity condition; additionally, if solutions of the function, which are related to the first-order time derivative, possess no poles nor algebraic branch points, then the maximal regularity of nonlinear second-order hyperbolic boundary differential equations exists. This study explores the use of taking the positive definite second-order operator as the generator of an analytic semi-group. We impose specific boundary conditions to make this positive definite second-order operator self-adjoint. As a linear operator, the self-adjoint operator satisfies the linearity property. This, in turn, facilitates the application of semi-group theory and linear operator theory. |
|---|---|
| ISSN: | 2075-1680 |