The Korteweg-de Vries equation on a metric star graph

Abstract

We prove local well-posedness for the Cauchy problem associated to Korteweg-de Vries equation on a metric star graph with three semi-infinite edges given by one negative half-line and two positives half-lines attached to a common vertex, for two classes of boundary conditions. The results are obtained in the low regularity setting by using the Duhamel Boundary Forcing Operator, in context of half-lines, introduced by Colliander, Kenig (2002),and extended by Holmer (2006) and Cavalcante (2017).

24 pages, 1 figure. A final version. Published in Zeitschrift für angewandte Mathematik und Physik

References in corpus (4)

• Ground state and orbital stability for the NLS equation on a general starlike graph with potentials
• On the Inverse Scattering Method for Integrable PDEs on a Star Graph
• Airy-type evolution equations on star graphs
• The initial-boundary value problem for Schrödinger-Korteweg-de Vries system on the half-line

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• Linear instability of stationary solutions for the Korteweg-de Vries equation on a star graph
• Lower regularity solutions of the biharmonic Schrödinger equation in a quarter plane
• Forcing operators on star graphs applied for the cubic fourth order Schrödinger equation
• Dynamical processes on metric networks
• The time-fractional Airy equation on the metric graphs
• Controllability for Schrödinger type system with mixed dispersion on compact star graphs
• The Korteweg-de Vries Equation on general star graphs
• Linearized Korteweg -- De Vries equation on a tree with unbounded root and edges
• Topologically induced spectral behavior: the example of quantum graphs