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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We undertake a regularity analysis of the solutions to initial/boundary valueproblems for the (third-order in time) Moore-Gibson-Thompson (MGT) equation.The key to the present investigation is that the MGT equation falls within alarge class of systems with memory, with affine term depending on a parameter.For this model equation a regularity theory is provided, which is of alsoindependent interest; it is shown in particular that the effect of boundarydata that are square integrable (in time and space) is the same displayed bywave equations. Then, a general picture of the (interior) regularity ofsolutions corresponding to homogeneous boundary conditions is specificallyderived for the MGT equation in various functional settings. This confirms thegain of one unity in space regularity for the time derivative of the unknown, afeature that sets the MGT equation apart from other PDE models for wavepropagation. The adopted perspective and method of proof enables us to attainas well the (sharp) regularity of boundary traces.

On the regularity of solutions to the Moore-Gibson-Thompson equation: a perspective via wave equations with memory