[NOVA Math] Seminar of Analysis

The Center of Mathematics and Applications (NOVA Math), promote the Seminar of Analysis with the title: “Analytical and numerical analysis of a parabolic partial differential equation involving the p(x)-bilaplacian operator”. Willian Panni (Center for Mathematics and Applications (NOVA Math) & Universidade da Beira Interior) is the speaker.

Abstract: In recent decades, differential equations with nonstandard growth conditions have attracted increasing attention from researchers. Such problems arise in various branches of applied mathematics and physics, including image restoration and digital processing, electrorheological or thermo-rheological fluid flows, and elasticity. At the intersection of these areas lies the study of problems involving the p(x)-bilaplacian operator. In this seminar, we investigate a parabolic partial differential equation with the p(x)-bilaplacian operator. By performing a change of variables, the original problem is reformulated as a system of two second-order equations. We discretize this system with respect to the variables t and x, leading to the semidiscrete and discrete problems, respectively. We establish existence, uniqueness, and a priori estimates for both the semidiscrete and the discrete solutions. Furthermore, we prove that the resulting system of second-order equations admits a unique weak solution. A detailed study of the convergence order of the semidiscrete and discrete solutions toward the weak solution is also presented. Finally, we present numerical examples in one-dimensional and two-dimensional spatial domains using MATLAB software. 

23/09/2025 (Tuesday), from 13:00 to 14:00, Room 3, Building  Hangar II.