Well-Posedness Results and Dissipative Limit of High Dimensional KdV-Type Equations

Author(s)

Carvajal, Xavier ^[1] ; Esfahani, Amin ^[2] ; Panthee, Mahendra ^[3]

Affiliation

^[1] Univ Fed Rio de Janeiro, Ilha Fundao, Ctr Technol, Inst Matemat, Av Horacio Macedo, BR-21941972 Rio de Janeiro, RJ - Brazil

^[2] Damghan Univ, Sch Math & Comp Sci, Damghan 36715364 - Iran

^[3] IMECC UNICAMP, Rua Sergio Buarque de Holanda, 651 Cidade Univ, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 48, n. 4, p. 505-550, DEC 2017.
• Web of Science Citations: 1

Abstract

Considered in this work is an n-dimensional dissipative version of the Korteweg-de Vries (KdV) equation. Our goal here is to investigate the well-posedness issue for the associated initial value problem in the anisotropic Sobolev spaces. We also study well-posedness behavior of this equation when the dissipative effects are reduced. (AU)

• FAPESP's process: 16/25864-6 - Nonlinear Evolution Equations of Dispersive Type
• Grantee: Mahendra Prasad Panthee
• Support Opportunities: Regular Research Grants
• FAPESP's process: 12/20966-4 - Well-posedness of the Cauchy problem and stability theory for nonlinear dispersive equations
• Grantee: Mahendra Prasad Panthee
• Support Opportunities: Regular Research Grants