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- Title
THE LIMIT OF BLOW-UP DYNAMICS SOLUTIONS FOR A CLASS OF NONLINEAR CRITICAL SCHRÖDINGER EQUATIONS.
- Authors
Jean-Jacques, N'takpe; Blin, L. Boua Sobo; Halima, Nachid; Gnowille, Kambire D.
- Abstract
This paper considers the asymptotic behavior of solutions of equations of evolutions, and concentrates on the analysis of the critical blow-up solutions for a class of evolutions for nonlinear Schrödinger equations in a bounded domain. More precisely, the numerical approximation of the blow-up rate below the one of the known explicit explosive solutions is studied, which has strictly positive energy for the following initial-boundary value problem: ... where ... is a complex-valued function of the variable x ∈ ℝd, Δ is the Laplace operator in ℝd and the time t ≥ The paper proposes a general setting to study and understand the behavior of the blow-up solutions in a finite time as a function of the parameters α, β, with initial condition u(0, x) = u0, in the energy space h¹ ∈ ℝd, also in the case where ℝd, is large enough and its size d is taken as parameter. Some assumptions are found under which the solution of the above problem blows-up in a finite time, study the dynamics of blow-up solutions and estimate its blow-up time. Finally, some numerical experiments to illustrate the analysis have been provided.
- Subjects
NONLINEAR Schrodinger equation; BLOWING up (Algebraic geometry); NONLINEAR evolution equations; EVOLUTION equations; FINITE difference method
- Publication
Advances in Differential Equations & Control Processes, 2024, Vol 31, Issue 2, p207
- ISSN
0974-3243
- Publication type
Article
- DOI
10.17654/0974324324011