21 citations · 68 across the 16 of their papers we have counts for
17 papers
Inverse Scattering for Critical Semilinear Wave Equations
Antônio Sá Barreto, Gunther Uhlmann, Yiran Wang
We show that the scattering operator for defocusing energy critical semilinear wave equations \square u+f(u)=0, with f C-infinity and f ~ u^5, in three space dimensions, determines…
Interactions of Semilinear Progressing Waves in Two or More Space Dimensions
Antonio Sa Barreto
We show that singularities form after the interaction of three transversal semilinear conormal waves. Our results hold for space dimensions two and higher, and for arbitrary smooth…
Singularities generated by the triple interaction of semilinear conormal waves
Antônio Sá Barreto, Yiran Wang
We study the local propagation of conormal singularities for solutions of semilinear wave equations , where is a polynomial of degree in $…
The scattering operator on asymptotically hyperbolic manifolds
Antônio Sá Barreto, Yiran Wang
We obtain a formula for the Schwartz kernel of the scattering operator in terms of the Schwartz kernel of the fundamental solution of the wave operator on asymptotically hyperbolic…
High Energy Resolvent Estimates on Conformally Compact Manifolds with Variable Curvature at Infinity
Antonio Sa Barreto, Yiran Wang
We construct a semiclassical parametrix for the resolvent of the Laplacian acing on functions on non-trapping conformally compact manifolds with variable sectional curvature at inf…
The Scattering Relation on Asymptotically Hyperbolic Manifolds
Antonio Sa Barreto, Yiran Wang
We study the scattering relation and the sojourn times on non-trapping asymptotically hyperbolic manifolds and use it to obtain the asymptotics of the distance function on geodesic…