Discover how the reduced wave equation behaves in complex domains and why boundary conditions matter for uniqueness.
This book examines foundational results about when a solution to the reduced wave equation is uniquely determined by its values and boundary data. It discusses extensions of classical theorems to more general shapes, such as exterior domains, finite and infinite boundaries, and surfaces with singularities. The material focuses on practical implications for diffraction theory, including how different boundary conditions influence existence and uniqueness.
- See how exterior domains and regular closed surfaces shape uniqueness results.
- Learn about alternative radiation conditions and their weaker forms.
- Understand how mixed boundary conditions extend classic theorems for diffraction problems.
- Explore how infinite boundaries and conical singularities are handled in the theory.
Ideal for readers of advanced applied mathematics and diffraction theory who seek a rigorous treatment of boundary-value problems and their impact on wave behavior.