17 citations · 38 across the 11 of their papers we have counts for
11 papers
Global existence for initial-boundary value problems of one-dimension quasilinear wave equations with null conditions
Dongbing Zha
We consider the initial-boundary value problems on for one-dimension systems of quasilinear wave equations with null conditions. We show that…
Scattering and Rigidity for Nonlinear Elastic Waves
Dongbing Zha
For the Cauchy problem of nonlinear elastic wave equations of three dimensional isotropic, homogeneous and hyperelastic materials satisfying the null condition, global existence of…
Global wellposedness for 2D quasilinear wave without Lorentz
Xinyu Cheng, Dong Li, Jiao Xu +1
We consider the two-dimensional quasilinear wave equations with standard null-form type quadratic nonlinearities. We prove global wellposedness without using the Lorentz boost vect…
On one-dimension quasilinear wave equations with null conditions
Dongbing Zha
In this paper, we show that one-dimension systems of quasilinear wave equations with null conditions admit global classical solutions for small initial data. This result extends Lu…
Global existence for a system of multiple-speed wave equations violating the null condition
Kunio Hidano, Kazuyoshi Yokoyama, Dongbing Zha
We discuss the Cauchy problem for a system of semilinear wave equations in three space dimensions with multiple wave speeds. Though our system does not satisfy the standard null co…
Global Nonlinear Stability of Geodesic Solutions of Evolutionary Faddeev Model
Jianli Liu, Dongbing Zha, Yi Zhou
In this paper, for evolutionary Faddeev model corresponding to maps from the Minkowski space to the unit sphere , we show the global nonlinear stab…
Remarks on a system of quasi-linear wave equations in D satisfying the weak null condition
Kunio Hidano, Dongbing Zha
We give an alternative proof of the global existence result originally due to Hidano and Yokoyama for the Cauchy problem for a system of quasi-linear wave equations in three space…
Global low regularity solutions for nonlinear elastic waves
Kunio Hidano, Dongbing Zha
We study the Cauchy problem for 3-D nonlinear elastic waves satisfying the null condition with low regularity initial data. In the radially symmetric case, we prove the global exis…
Space-time estimates, regularity and almost global existence for elastic waves
Kunio Hidano, Dongbing Zha
In this paper, we first establish a kind of weighted space-time estimate, which belongs to Keel-Smith-Sogge type estimates, for perturbed linear elastic wave equations. This…
Remarks on Nonlinear Elastic Waves in the Radial Symmetry in 2-D
Dongbing Zha
In this manuscript we first give the explicit variational structure of the nonlinear elastic waves for isotropic, homogeneous, hyperelastic materials in 2-D. Based on this variatio…
Lifespan of Classical Solutions to Quasilinear Wave Equations Outside of a Star-Shaped Obstacle in Four Space Dimensions
Dongbing Zha, Yi Zhou
We study the initial-boundary value problem of quasilinear wave equations outside of a star-shaped obstacle in four space dimensions, in which the nonlinear term under consideratio…