Holzegel, Gustav; Shao, Arick The bulk-boundary correspondence for the Einstein equations in asymptotically anti-de Sitter spacetimes. (English) Zbl 1523.83002 Arch. Ration. Mech. Anal. 247, No. 3, Paper No. 56, 77 p. (2023). MSC: 83C05 83C30 83F05 53C18 41A60 53C21 PDFBibTeX XMLCite \textit{G. Holzegel} and \textit{A. Shao}, Arch. Ration. Mech. Anal. 247, No. 3, Paper No. 56, 77 p. (2023; Zbl 1523.83002) Full Text: DOI arXiv
Shao, Arick; Vergara, Bruno Approximate boundary controllability for parabolic equations with inverse square infinite potential wells. arXiv:2311.01628 Preprint, arXiv:2311.01628 [math.AP] (2023). BibTeX Cite \textit{A. Shao} and \textit{B. Vergara}, ``Approximate boundary controllability for parabolic equations with inverse square infinite potential wells'', Preprint, arXiv:2311.01628 [math.AP] (2023) Full Text: arXiv OA License
Guisset, Simon; Shao, Arick On counterexamples to unique continuation for critically singular wave equations. arXiv:2308.03525 Preprint, arXiv:2308.03525 [math.AP] (2023). MSC: 35L05 35A02 81T35 BibTeX Cite \textit{S. Guisset} and \textit{A. Shao}, ``On counterexamples to unique continuation for critically singular wave equations'', Preprint, arXiv:2308.03525 [math.AP] (2023) Full Text: arXiv OA License
Cha, Louis Dongbing; Shao, Arick Global stability of traveling waves for \((1+1)\)-dimensional systems of quasilinear wave equations. (English) Zbl 1517.35037 J. Hyperbolic Differ. Equ. 19, No. 4, 549-586 (2022). MSC: 35B40 35L52 35L72 PDFBibTeX XMLCite \textit{L. D. Cha} and \textit{A. Shao}, J. Hyperbolic Differ. Equ. 19, No. 4, 549--586 (2022; Zbl 1517.35037) Full Text: DOI arXiv
Chatzikaleas, Athanasios; Shao, Arick A gauge-invariant unique continuation criterion for waves in asymptotically anti-de Sitter spacetimes. (English) Zbl 1510.83026 Commun. Math. Phys. 395, No. 2, 521-570 (2022). MSC: 83C45 81T32 53C18 53C22 70S15 83C05 35G20 PDFBibTeX XMLCite \textit{A. Chatzikaleas} and \textit{A. Shao}, Commun. Math. Phys. 395, No. 2, 521--570 (2022; Zbl 1510.83026) Full Text: DOI arXiv
McGill, Alex; Shao, Arick Null geodesics and improved unique continuation for waves in asymptotically anti-de Sitter spacetimes. (English) Zbl 1480.83030 Classical Quantum Gravity 38, No. 5, Article ID 054001, 63 p. (2021). MSC: 83C30 35L05 81Q05 81R20 53C22 53C18 58J32 83C15 53C25 35Q75 PDFBibTeX XMLCite \textit{A. McGill} and \textit{A. Shao}, Classical Quantum Gravity 38, No. 5, Article ID 054001, 63 p. (2021; Zbl 1480.83030) Full Text: DOI arXiv
Enciso, Alberto; Shao, Arick; Vergara, Bruno Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials. (English) Zbl 1467.35067 J. Eur. Math. Soc. (JEMS) 23, No. 10, 3459-3495 (2021). MSC: 35B45 35L15 35L81 93B07 PDFBibTeX XMLCite \textit{A. Enciso} et al., J. Eur. Math. Soc. (JEMS) 23, No. 10, 3459--3495 (2021; Zbl 1467.35067) Full Text: DOI arXiv
Enciso, Alberto; Shao, Arick; Vergara, Bruno Controllability of parabolic equations with inverse square infinite potential wells via global Carleman estimates. arXiv:2112.04457 Preprint, arXiv:2112.04457 [math.AP] (2021). BibTeX Cite \textit{A. Enciso} et al., ``Controllability of parabolic equations with inverse square infinite potential wells via global Carleman estimates'', Preprint, arXiv:2112.04457 [math.AP] (2021) Full Text: arXiv OA License
Jena, Vaibhav Kumar; Shao, Arick Control of waves on Lorentzian manifolds with curvature bounds. arXiv:2112.09539 Preprint, arXiv:2112.09539 [math.AP] (2021). BibTeX Cite \textit{V. K. Jena} and \textit{A. Shao}, ``Control of waves on Lorentzian manifolds with curvature bounds'', Preprint, arXiv:2112.09539 [math.AP] (2021) Full Text: arXiv OA License
Holzegel, Gustav; Shao, Arick Unique continuation from infinity in asymptotically anti-de Sitter spacetimes. II: Non-static boundaries. (English) Zbl 1385.83002 Commun. Partial Differ. Equations 42, No. 12, 1871-1922 (2017). MSC: 83C05 35L05 81Q05 83C25 35Q75 53Z05 PDFBibTeX XMLCite \textit{G. Holzegel} and \textit{A. Shao}, Commun. Partial Differ. Equations 42, No. 12, 1871--1922 (2017; Zbl 1385.83002) Full Text: DOI arXiv Link
Alexakis, Spyros; Shao, Arick On the profile of energy concentration at blow-up points for subconformal focusing nonlinear waves. (English) Zbl 1377.35199 Trans. Am. Math. Soc. 369, No. 8, 5525-5542 (2017). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 35L71 35B44 PDFBibTeX XMLCite \textit{S. Alexakis} and \textit{A. Shao}, Trans. Am. Math. Soc. 369, No. 8, 5525--5542 (2017; Zbl 1377.35199) Full Text: DOI arXiv
Holzegel, Gustav; Shao, Arick Unique continuation from infinity in asymptotically anti-de Sitter spacetimes. (English) Zbl 1351.83009 Commun. Math. Phys. 347, No. 3, 723-775 (2016). MSC: 83C05 35L05 53Z05 83C25 35Q75 PDFBibTeX XMLCite \textit{G. Holzegel} and \textit{A. Shao}, Commun. Math. Phys. 347, No. 3, 723--775 (2016; Zbl 1351.83009) Full Text: DOI arXiv
Alexakis, Spyros; Shao, Arick Bounds on the Bondi energy by a flux of curvature. (English) Zbl 1346.83025 J. Eur. Math. Soc. (JEMS) 18, No. 9, 2045-2106 (2016). MSC: 83C30 35Q75 83C05 53C12 53C21 83C40 83C57 PDFBibTeX XMLCite \textit{S. Alexakis} and \textit{A. Shao}, J. Eur. Math. Soc. (JEMS) 18, No. 9, 2045--2106 (2016; Zbl 1346.83025) Full Text: DOI arXiv
Alexakis, Spyros; Schlue, Volker; Shao, Arick Unique continuation from infinity for linear waves. (English) Zbl 1329.35087 Adv. Math. 286, 481-544 (2016). MSC: 35B60 35B45 35Q75 35A02 PDFBibTeX XMLCite \textit{S. Alexakis} et al., Adv. Math. 286, 481--544 (2016; Zbl 1329.35087) Full Text: DOI arXiv
Alexakis, Spyros; Shao, Arick Global uniqueness theorems for linear and nonlinear waves. (English) Zbl 1329.35007 J. Funct. Anal. 269, No. 11, 3458-3499 (2015). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 35A02 35L05 35B45 78A40 35B60 PDFBibTeX XMLCite \textit{S. Alexakis} and \textit{A. Shao}, J. Funct. Anal. 269, No. 11, 3458--3499 (2015; Zbl 1329.35007) Full Text: DOI arXiv
Alexakis, Spyros; Shao, Arick On the geometry of null cones to infinity under curvature flux bounds. (English) Zbl 1304.83005 Classical Quantum Gravity 31, No. 19, Article ID 195012, 62 p. (2014). MSC: 83C05 83C75 83C40 83C57 83C10 53Z05 PDFBibTeX XMLCite \textit{S. Alexakis} and \textit{A. Shao}, Classical Quantum Gravity 31, No. 19, Article ID 195012, 62 p. (2014; Zbl 1304.83005) Full Text: DOI arXiv
Egli, Daniel; Fröhlich, Jürg; Gang, Zhou; Shao, Arick; Sigal, Israel Michael Hamiltonian dynamics of a particle interacting with a wave field. (English) Zbl 1281.35084 Commun. Partial Differ. Equations 38, No. 12, 2155-2198 (2013). MSC: 35Q70 35B35 70H14 35B40 35C07 PDFBibTeX XMLCite \textit{D. Egli} et al., Commun. Partial Differ. Equations 38, No. 12, 2155--2198 (2013; Zbl 1281.35084) Full Text: DOI arXiv