2017/12/28 by Francesca Bucci, Bucci, Francesca, Luciano Pandolfi +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods for differential equations #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1712.09930
openalex publication_date 2017/12/28 · openalex created_date 2022/08/16 · openalex updated_date 2026/07/28
We undertake a regularity analysis of the solutions to initial/boundary value\nproblems for the (third-order in time) Moore-Gibson-Thompson (MGT) equation.\nThe key to the present investigation is that the MGT equation falls within a\nlarge class of systems with memory, with affine term depending on a parameter.\nFor this model equation a regularity theory is provided, which is of also\nindependent interest; it is shown in particular that the effect of boundary\ndata that are square integrable (in time and space) is the same displayed by\nwave equations. Then, a general picture of the (interior) regularity of\nsolutions corresponding to homogeneous boundary conditions is specifically\nderived for the MGT equation in various functional settings. This confirms the\ngain of one unity in space regularity for the time derivative of the unknown, a\nfeature that sets the MGT equation apart from other PDE models for wave\npropagation. The adopted perspective and method of proof enables us to attain\nas well the (sharp) regularity of boundary traces.\n