Contribution to the Qualitative Study of Some Generalized Boussinesq Problems

Garti, Ines (2024) Contribution to the Qualitative Study of Some Generalized Boussinesq Problems. Doctoral thesis, Université Mohamed Khider (Biskra - Algérie).

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Abstract

Research on Boussinesq equations has grown considerably over the past three decades due to their adaptability in explaining nonlinear phenomena, particularly in the analysis of water wave dynamics. These equations are widely used in various …elds, including the study of oceanic waves and coastal engineering. This thesis explores the existence and …nite-time blow-up of solutions in the Cauchy problem associated with a generalized Boussinesq equation. The study of the generalized Boussinesq equation and its solutions, including existence, non-existence, and blow-up, is of great interest. The thesis investigates solutions in both bounded and unbounded domains, as well as in the presence of logarithmic nonlinearity. Local solutions are proven to exist and be unique in both cases. Under certain restrictions on the initial data of our problems, we establish the existence and uniqueness of global solutions, as well as the possibility of blowing up solutions in …nite time.

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