scholarly journals A Note on Local Well-Posedness of Generalized KdV Type Equations with Dissipative Perturbations

2017 ◽  
pp. 85-100 ◽  
Author(s):  
Xavier Carvajal ◽  
Mahendra Panthee
Keyword(s):  
Well Posedness ◽  
Kdv Type Equations

scholarly journals Sharp local well-posedness of KdV type equations with dissipative perturbations

2016 ◽  
Vol 74 (3) ◽  
pp. 571-594 ◽  
Author(s):  
Xavier Carvajal ◽  
Mahendra Panthee
Keyword(s):  
Well Posedness ◽  
Kdv Type Equations

scholarly journals Local well-posedness of the fifth-order KdV-type equations on the half-line

2019 ◽  
Vol 18 (5) ◽  
pp. 2607-2661 ◽  
Author(s):  
Márcio Cavalcante ◽  
◽  
Chulkwang Kwak ◽  
Keyword(s):  
Half Line ◽  
Well Posedness ◽  
Kdv Type Equations ◽  
Fifth Order

scholarly journals Global well-posedness for a system of KdV-type equations with coupled quadratic nonlinearities

2014 ◽  
Vol 215 ◽  
pp. 67-149 ◽  
Author(s):  
Jerry L. bona ◽  
Jonathan Cohen ◽  
Gang Wang
Keyword(s):  
Initial Data ◽  
Sobolev Spaces ◽  
Initial Value Problem ◽  
Coupled Systems ◽  
Well Posedness ◽  
Initial Value ◽  
Quadratic Polynomials ◽  
Partial Differentiation ◽  
Quadratic Nonlinearities ◽  
Kdv Type Equations

AbstractIn this paper, coupled systemsof Korteweg-de Vries type are considered, where u = u(x, t), v = v(x, t) are real-valued functions and where x, t∈R. Here, subscripts connote partial differentiation andare quadratic polynomials in the variables u and v. Attention is given to the pure initial-value problem in which u(x, t) and v(x, t) are both specified at t = 0, namely,for x ∈ ℝ. Under suitable conditions on P and Q, global well-posedness of this problem is established for initial data in the L2-based Sobolev spaces Hs(ℝ) × Hs(ℝ) for any s > ‒3/4.

scholarly journals Global well-posedness for a system of KdV-type equations with coupled quadratic nonlinearities

2014 ◽  
Vol 215 ◽  
pp. 67-149 ◽  
Author(s):  
Jerry L. bona ◽  
Jonathan Cohen ◽  
Gang Wang
Keyword(s):  
Initial Data ◽  
Sobolev Spaces ◽  
Initial Value Problem ◽  
Coupled Systems ◽  
Well Posedness ◽  
Initial Value ◽  
Quadratic Polynomials ◽  
Partial Differentiation ◽  
Quadratic Nonlinearities ◽  
Kdv Type Equations

AbstractIn this paper, coupled systemsof Korteweg-de Vries type are considered, whereu=u(x, t),v=v(x, t) are real-valued functions and wherex, t∈R. Here, subscripts connote partial differentiation andare quadratic polynomials in the variablesuandv. Attention is given to the pure initial-value problem in whichu(x, t) andv(x, t) are both specified att= 0, namely,forx∈ ℝ. Under suitable conditions onPandQ, global well-posedness of this problem is established for initial data in theL2-based Sobolev spacesHs(ℝ) ×Hs(ℝ) for anys> ‒3/4.

scholarly journals Well-posedness for KdV-type equations with quadratic nonlinearity

2019 ◽  
Vol 20 (3) ◽  
pp. 811-835
Author(s):  
Hiroyuki Hirayama ◽  
Shinya Kinoshita ◽  
Mamoru Okamoto
Keyword(s):  
Quadratic Nonlinearity ◽  
Well Posedness ◽  
Kdv Type Equations
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