English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We examine the analytic extension of solutions of linear,constant-coefficient initial-boundary value problems outside their spatialdomain of definition. We use the Unified Transform Method or Method of Fokas,which gives a representation for solutions to half-line and finite-intervalinitial-boundary value problems as integrals of kernels with explicit spatialand temporal dependence. These solution representations are defined within thespatial domain of the problem. We obtain the extension of these representationformulae via Taylor series outside these spatial domains and find the extensionof the initial condition that gives rise to a whole-line initial-value problemsolved by the extended solution. In general, the extended initial condition isnot differentiable or continuous unless the boundary and initial conditionssatisfy compatibility conditions. We analyze dissipative and dispersiveproblems, and problems with continuous and discrete spatial variables.

The analytic extension of solutions to initial-boundary value problems outside their domain of definition