Global existence for the Benjamin-Bona-Mahony equation in arbitrary dimensions

About the Benjamin-Bona-Mahony Equation in Domains with Moving Boundary

“…Later was the time for Bona & Dougalis [5] prove the existence and uniqueness of solutions for the BBM equation considering non-homogeneous boundary conditions. The case n dimensional of the equation (1.2) was studied by Goldstein [8] and again in the work of Avrin and Goldstein together [1]. Similar equations to (1.2) in noncylindrical domains were studied by Cousin and Larkin for the Kuramoto Sivashinski equation [7] and recently Barreto et al [2] for the Rosenau and BBM equations.…”

Averaging of the 3D non-autonomous Benjamin-Bona-Mahony equation with singularly oscillating forces

“…China. 2 College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, P.R. China.…”

On Blowup of a Solution to a Sobolev-Type Equation with a Nonlocal Source

“…Observe that dissipative quasilinear wave equations with and without sources were studied in [15][16][17][18][19][20][21][22][23]. These articles address the questions of the asymptotic behavior of solutions to pseudoparabolic equations at large times and the questions of existence of solitary-wave type solutions and their stability.…”