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Texas A&M University
Mathematics

Events for 03/02/2021 from all calendars

Nonlinear Partial Differential Equations

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Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Makram Hamouda, Imam Abdulrahman Bin Faisal University

Title: Some blow-up problems related to the semilinear wave equation with the scale-invariant damping and mass terms

Abstract: In this talk we discuss some blow-up results in connection with the semilinear wave equation in the scale-invariant case with time-dependent dissipation, mass term and power nonlinearity. Under the assumption of small initial data, we study the influence of the damping and mass terms in the global dynamics of the solution. In the first part, we start by the massless case where we obtain a new interval for the damping parameter that we conjecture to be closer to optimality, or probably optimal, and, thus, characterizes the threshold between the blow-up and the global existence regions. For example, the new blow-up region is now a shifting of the well-known Glassey exponent in the case of time derivative nonlinearity. Similar results are obtained for the other nonlinearities as well. The second part will be devoted to the same model but with mass term. In addition to the theoretical results, some simple numerical simulations for this case will be presented too.