Scattering for the quasilinear wave equations with null conditions in two dimensions
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2020.02.024
Abstract: Abstract We give a detailed description of the scattering theory of solutions to the quasilinear wave equations with null conditions and small initial data in two dimensions. The scattering profile is shown to be the… read more here.
Keywords: quasilinear wave; dimensions scattering; null conditions; equations null ... See more keywords
On Global Solvability of One-Dimensional Quasilinear Wave Equations
Sign Up to like & getrecommendations! Published in 2020 at "Lobachevskii Journal of Mathematics"
DOI: 10.1134/s1995080220120422
Abstract: The paper concerns global solvability of initial value problem for one class of hyperbolic quasilinear second order equations with two independent variables, which have a rather wide range of applications. Besides existence and uniqueness of… read more here.
Keywords: dimensional quasilinear; solvability; quasilinear wave; solvability one ... See more keywords
Global nonexistence of solutions for a quasilinear wave equation with acoustic boundary conditions
Sign Up to like & getrecommendations! Published in 2017 at "Boundary Value Problems"
DOI: 10.1186/s13661-017-0773-1
Abstract: AbstractWe consider the quasilinear wave equation utt−△ut−div(|∇u|α−2∇u)−div(|∇ut|β−2∇ut)+a|ut|m−2ut=b|u|p−2u$$u_{tt} -\triangle u_{t} -\operatorname{div}\bigl(\vert \nabla u\vert ^{\alpha-2} \nabla u\bigr) - \operatorname{div}\bigl(\vert \nabla u_{t}\vert ^{\beta-2} \nabla u_{t} \bigr) +a \vert u_{t}\vert ^{m-2} u_{t} =b|u|^{p-2} u $$a,b>0$a,b>0$, associated with initial and… read more here.
Keywords: quasilinear wave; global nonexistence; boundary conditions; acoustic boundary ... See more keywords