Blar i NTNU Open på forfatter "Xue, Jun"
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Instability of the solitary waves for the generalized Boussinesq equations
Li, Bing; Ohta, Masahito; Wu, Yifei; Xue, Jun (Peer reviewed; Journal article, 2020)In this work, we consider the following generalized Boussinesq equation \begin{align*} \partial_{t}^2u-\partial_{x}^2u+\partial_{x}^2(\partial_{x}^2u+|u|^{p}u)=0,\qquad (t,x)\in\R\times \R, \end{align*} with $0<p<\infty$. ... -
One-sided Hölder regularity of global weak solutions of negative order dispersive equations
Mæhlen, Ola Isaac Høgåsen; Xue, Jun (Peer reviewed; Journal article, 2023)We prove global existence, uniqueness and stability of entropy solutions with initial data for a general family of negative order dispersive equations. These weak solutions are found to satisfy one-sided Hölder conditions ... -
Optimal small data scattering for the generalized derivative nonlinear Schrödinger equations
Bai, Ruobing; Wu, Yifei; Xue, Jun (Peer reviewed; Journal article, 2020)In this work, we consider the following generalized derivative nonlinear Schr\"odinger equation \begin{align*} i\partial_t u+\partial_{xx} u +i |u|^{2\sigma}\partial_x u=0, \quad (t,x)\in \R\times \R. \end{align*} We prove ... -
Periodic Hölder waves in a class of negative-order dispersive equations
Hildrum, Fredrik; Xue, Jun (Peer reviewed; Journal article, 2023)We prove the existence of highest, cusped, periodic travelling-wave solutions with exact and optimal α-Hölder continuity in a class of fractional negative-order dispersive equations of the form��+(|D|−��+�(�))�=0for every ... -
Solutions in Dispersive Equations and Steady Waves with Vorticity
Xue, Jun (Doctoral theses at NTNU;2023:292, Doctoral thesis, 2023) -
Solutions to ordinary differential equations at infinity
Kristengård, Silje Heggen (Bachelor thesis, 2022)I denne teksten skal vi se på løsninger til førsteordens ordinære differensiallikninger når t går mot uendelig. Vi vil ts for oss tre tilfeller av ordniære differensiallikninger og se på hva slags kriterier vi trenger for ...