Publications A. Rendall

Mathematical biology

(with P. Brechmann) Dynamics of the Selkov oscillator. To appear in Math. Biosci. Preprint version.

(with J. Werner, N. Sfakianakis and E. Griebeler) Energy intake functions and energy budgets of ectotherms and endotherms derived from their ontogenetic growth in body mass and timing of sexual maturation. J. Theor. Biol. 444, 83-92 (2018).

A Calvin bestiary. In Gurevich, P., Hell, J., Sanstede, B. and Scheel, A. (Eds.) Patterns of Dynamics. Springer, Berlin (2017). Preprint version.

(with E. D. Sontag) Multiple steady states and the form of response functions to antigen in a model for the initiation of T cell activation. R. Soc. open sci. 2017 4 170821. Preprint version.

(with J. Hell) Dynamical features of the MAPK cascade. In Graw, F., Matthäus, F. und Pahle, J. (Eds.) Modelling cellular systems. Springer, Berlin (2017). Preprint version.

(with D. Möhring) Overload breakdown in models for photosynthesis. Dyn. Sys. 32, 234-248 (2017). Preprint version.

(with S. Disselnkötter) Stability of stationary solutions in models of the Calvin cycle. Nonlin. Analysis RWA. 34, 481-494 (2017). Preprint version.

(with J. Hell) Sustained oscillations in the MAP kinase cascade. Math. Biosci. 282:162-173 (2016). Preprint version.

(with J. Hell) A proof of bistability for the dual futile cycle. Nonlin. Analysis: RWA. 24, 175-189 (2015). Preprint version.

(with J. J. L. Velázquez) Dynamical properties of models for the Calvin cycle. J. Dyn. Diff. Eq. 26, 673-705 (2014). Preprint version.

Multiple steady states in a mathematical model for interactions between T cells and macrophages. Disc. Cont. Dyn. Sys. B. 18, 769-782 (2013). Preprint version.

Mathematics of the NFAT signalling pathway. SIAM J. Appl. Dyn. Sys. 11, 988-1006 (2012). Preprint version.

Analysis of a mathematical model for interactions between T cells and macrophages. Electr. J. Diff. Eq. 2010, 115 (2010). Preprint version.

 

Book

Partial differential equations in general relativity. Oxford University Press, Oxford (2008). I maintain a page with errata and I am grateful for being informed about any mistakes readers find.

 

General relativity and gravity

(with J. J. L. Velázquez) Veiled singularities for the spherically symmetric massless Einstein-Vlasov system. Ann. H. Poincaré 18, 3565-3631 (2017). Preprint version

(with M. Dafermos) Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter. Commun. Pure Appl. Math. 69, 815-908 (2016). Preprint version

Construction of oscillatory singularities. In Garcia-Parrado, A., Mena, F. C., Moura, F. and Vaz, E.  (Eds.) description. Proceedings of the Spanish Relativity Meeting ERE2012, Guimaraes. Springer, Berlin (2014). Preprint version

(with H. Lee) The spatially homogeneous relativistic Boltzmann equation with a hard potential. Commun. PDE 38, 2238-2262 (2013). Preprint version.

(with S. Liebscher and S. B. Tchapnda) Oscillatory singularities in Bianchi models with magnetic fields. Ann. H. Poincaré 14, 1043-1075 (2013). Preprint version.

(with H. Lee) The Einstein-Boltzmann system and positivity. J. Hyp. Diff. Eq. 10, 77-104 (2013). Preprint version.

Dynamics of solutions of the Einstein equations with twisted Gowdy symmetry. J. Geom. Phys. 62, 569-577 (2012).  Preprint version.

(with P. G. LeFloch) A global foliation of Einstein-Euler spacetimes with Gowdy symmetry on T3. Arch. Rat. Mech. Anal. 201, 841-870 (2011). Preprint version.

(with J. J. L. Velázquez) A class of dust-like self-similar solutions of the massless Einstein-Vlasov system. Ann. H. Poincaré 12, 919-964 (2011). Preprint version.

(with H. J. Hwang and J. J. L. Velázquez) Optimal gradient estimates and asymptotic behaviour for the Vlasov-Poisson system with small initial data. Arch. Rat. Mech. Anal. 200, 313-360 (2011). Preprint version.

(with P. T. Allen) Asymptotics of linearized cosmological perturbations. J. Hyp. Diff. Eq. 7, 255-277 (2010). Preprint version.

(with A. Gödeke) Future geodesic completeness of some spatially homogeneous solutions of the vacuum Einstein equations in higher dimensions. Class. Quantum Grav. 27, 155019 (2010). Preprint version.

(with E. Nungesser) Strong cosmic censorship for solutions of the Einstein-Maxwell equations with polarized Gowdy symmetry. Class. Quantum Grav. 26, 105019 (2009). Preprint version.

(with F. Ståhl) Shock waves in plane symmetric spacetimes. Commun. PDE 33, 2020-2039 (2008). Preprint version.

(with N. Berndt) Isotropization in the approach to big rip singularities for Cardassian models. Class. Quantum Grav. 25, 145007 (2008). Preprint version.

Late-time oscillatory behaviour for self-gravitating scalar fields. Class. Quantum Grav. 24, 667-677 (2007). Preprint version.

(with J. M. Heinzle) Power-law inflation in spacetimes without symmetry. Commun. Math. Phys. 269, 1-15 (2007). Preprint version.

(with D. Tegankong) On the nature of initial singularities for solutions of the Einstein-Vlasov-scalar field system with surface symmetry. Math. Proc. Camb. Phil. Soc. 141, 547-562 (2006). Preprint version.

(with S. Bauer, M. Kunze and G. Rein) Multipole radiation in a collisionless gas coupled to electromagnetism or scalar gravitation. Commun. Math. Phys. 266, 267-288 (2006). Preprint version.

Mathematical properties of cosmological models with accelerated expansion. In Frauendiener, J., Giulini, D. J. W. and Perlick, V. (eds) Analytical and numerical approaches to mathematical relativity. Lecture Notes in Physics 692. Springer, Berlin (2006). Preprint version.

Dynamics of k-essence. Class. Quantum Grav. 23, 1557-1569 (2006). Preprint version.

(with J. M. Heinzle and C. Uggla) Theory of Newtonian self-gravitating stationary spherically symmetric systems. Math. Proc. Camb. Phil. Soc. 140, 177-192 (2006). Preprint version.

(with M. Dafermos) Inextendibility of expanding cosmological models with symmetry. Class. Quantum Grav. 22, L143-L147 (2005). Preprint version.

Theorems on existence and global dynamics for the Einstein equations. Living Reviews in Relativity lrr-2005-6 (2005). Preprint version.

The nature of spacetime singularities. In Ashtekar, A.: 100 years of relativity. Spacetime structure: Einstein and beyond. World Scientific, Singapore (2005). Preprint version.

Intermediate inflation and the slow-roll approximation. Class. Quantum Grav. 22, 1655-1666 (2005). Preprint version.

(with M. Dafermos) An extension principle for the Einstein-Vlasov system in spherical symmetry. Ann. H. Poincaré 6, 1137-1155 (2005). Preprint version.

(with D. Tegankong and N. Noutchegueme) Local existence and continuation criteria for solutions of the Einstein-Vlasov-scalar field system with surface symmetry. J. Hyp. Diff. Eq. 1, 691-724 (2004). Preprint version.

Asymptotics of solutions of the Einstein equations with positive cosmological constant. Ann. H. Poincaré 5, 1041-1064 (2004). Preprint version.

Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound. Class. Quantum Grav. 21, 2445 - 2454 (2004). Preprint version.

Fuchsian methods and spacetime singularities. Class. Quantum Grav. 21, S295-S304 (2004). Preprint version.

(with P. Noundjeu and N. Noutchegueme) Existence of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system. J. Math. Phys. 45, 668-676 (2004). Preprint version.

(with H. Andréasson and M. Weaver) Existence of CMC and constant areal time foliations in T^2 symmetric spacetimes with Vlasov matter. Commun. PDE 29, 237-262 (2004). Preprint version.

The Einstein-Vlasov system. In Chruściel, P. T. and Friedrich, H. (eds.) The Einstein equations and the large scale behavior of gravitational fields. Birkhauser, Basel (2004). Preprint version.

(with S. B. Tchapnda) Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant. Class. Quantum Grav. 20, 3037-3049 (2003). Preprint version.

(with H. Andréasson and G. Rein) On the Einstein-Vlasov system with hyperbolic symmetry. Math. Proc. Camb. Phil. Soc. 134, 529-549 (2003). Preprint version.

Theorems on existence and global dynamics for the Einstein equations. Living Reviews in Relativity 5, 6 (2002). Preprint version.

(with T. Damour, M. Henneaux and M. Weaver) Kasner-like behaviour for subcritical Einstein-matter systems. Ann. H. Poincaré 3, 1049-1111 (2002). Preprint version.

Cosmological models and centre manifold theory. Gen. Rel. Grav. 34, 1277-1294 (2002). Preprint version.

Applications of the theory of evolution equations to general relativity. In Bishop, N. T. and Maharaj, S. N. (eds) Proceedings of the 16th International Conference on General Relativity and Gravitation. World Scientific, 2002. Preprint version.

(with M. Kunze) Simplified models of electromagnetic and gravitational radiation damping. Class. Quantum Grav. 18, 3573-3587 (2001). Preprint version.

(with M. Weaver) Manufacture of Gowdy spacetimes with spikes. Class. Quantum Grav. 18, 2959-2975 (2001). Preprint version.

(with M. Kunze) The Vlasov-Poisson system with radiation damping. Ann. H. Poincaré 2, 857-886 (2001). Preprint version.

(with L. Andersson) Quiescent cosmological singularities. Commun. Math. Phys. 218, 479-511 (2001). Preprint version.

Blow-up for solutions of hyperbolic PDE and spacetime singularities. In Depauw, N., Robert, D. and Saint Raymond, X. (eds) Journées Equations aux Dérivées Partielles, Nantes, 2000. CNRS, Nantes. Preprint version.

(with C. Uggla) Dynamics of spatially homogeneous locally rotationally symmetric solutions of the Einstein-Vlasov equations. Class. Quantum Grav. 17, 4697-4713 (2000). Preprint version.

Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity. Class. Quantum Grav. 17, 3305-3316 (2000). Preprint version.

(with H. Friedrich) The Cauchy problem for the Einstein equations. In B. G. Schmidt (ed) Einstein's Field Equations and Their Physical Implications. Lecture Notes in Physics 540. Springer, Berlin (2000). Preprint version.

Local and global existence theorems for the Einstein equations. Living Reviews in Relativity 3, 1 (2000).  Preprint version.

(with G. Rein) Compact support of spherically symmetric equilibria in non-relativistic and relativistic galactic dynamics. Math. Proc. Camb. Phil. Soc. 128, 363-380 (2000). Preprint version.

(with K. P. Tod) Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric. Class. Quantum Grav. 16, 1705-1726 (1999). Preprint version.

(with G. Rein and J. Schaeffer) Critical collapse of collisionless matter - a numerical investigation. Phys. Rev. D58, 044007 (1998). Preprint version.

The structure of singularities in inhomogeneous cosmological models. In Rainer, M., Schmidt, H.-J. (eds) Current topics in mathematical cosmology, pp. 118-122. World Scientific, 1998. Preprint version.

(with J. Isenberg) Cosmological spacetimes not covered by a constant mean curvature slicing. Class. Quantum Grav. 15, 3679-3688 (1998). Preprint version.

Compact null hypersurfaces and collapsing Riemannian manifolds. Mathematische Nachrichten 193, 111-118 (1998). Preprint version.

Local and global existence theorems for the Einstein equations. Living Reviews in Relativity 1, 4 (1998). Preprint version.

(with S. Kichenassamy) Analytic description of singularities in Gowdy spacetimes. Class. Quantum Grav. 15, 1339-1355 (1998). Preprint version.

Global dynamics of the Mixmaster model. Class. Quantum Grav. 14, 2341-2356 (1997). Preprint version.

Existence and non-existence results for global constant mean curvature foliations. Nonlinear Analysis, Theory, Methods and Applications 30, 3589-3598 (1997). Preprint version.

Existence of constant mean curvature hypersurfaces in spacetimes with two-dimensional local symmetry. Commun. Math. Phys. 159, 145-164 (1997). Preprint version.

An introduction to the Einstein-Vlasov system. Banach Centre Publications 41, 35-68 (1997). Preprint version.

Solutions of the Einstein equations with matter. In M. Francaviglia, G. Longhi, L. Lusanna, E. Sorace (eds.) Proceedings of the 14th International Conference on General Relativity and Gravitation, pp.313-335. World Scientific, 1997. Preprint version.

Constant mean curvature foliations in cosmological spacetimes. Helvet. Phys. Acta 69, 490-500 (1996). Preprint version.

(with G. A. Burnett) Existence of maximal hypersurfaces in some spherically symmetric spacetimes. Class. Quantum Grav. 13, 111-123 (1996). Preprint version.

The initial singularity in solutions of the Einstein-Vlasov system of Bianchi type I. J. Math Phys. 37, 438-451 (1996). Preprint version.

Global properties of locally spatially homogeneous cosmological models with matter. Math. Proc. Camb. Phil. Soc. 118, 511-526 (1995). Preprint version.

(with P. Chruściel) Strong cosmic censorship in vacuum space-times with compact locally homogeneous Cauchy surfaces. Ann. Phys. 242, 349-385 (1995). Preprint version.

Crushing singularities in spacetimes with spherical, plane and hyperbolic symmetry. Class. Quantum Grav. 12, 1517-1533 (1995). Preprint version.

On the nature of singularities in plane symmetric scalar field cosmologies. Gen. Rel. Grav. 27, 213-221 (1995). Preprint version.

(with G. Rein and J. Schaeffer) A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system. Commun. Math. Phys. 168, 467-478 (1995). Preprint version.

Adjointness relations as a criterion for choosing an inner product. In: J. Ehlers, H. Friedrich (eds.), Canonical gravity: from classical to quantum (Springer: Berlin 1994). Preprint version.

(with U. Brauer and O. Reula) The cosmic no-hair theorem and the nonlinear stability of homogeneous Newtonian cosmological models. Class. Quantum Grav. 11, 2283-2296 (1994). Preprint version.

(with G. Rein) Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting. Arch. Rat. Mech. Anal. 126, 183-201 (1994). Preprint version.

Cosmic censorship for some spatially homogeneous cosmological models. Ann. Phys. 233, 82-96 (1994). Preprint version.

The Newtonian limit for asymptotically flat solutions of the Vlasov-Einstein system. Commun. Math. Phys. 163:89-112 (1994). Preprint version.

Unique determination of an inner product by adjointness relations in the algebra of quantum observables. Class. Quantum Grav. 10:2261-2269 (1993). Preprint version.

(with J. Rauch) Blow-up of test fields near Cauchy horizons. Lett. Math. Phys. 29:241-248 (1993). Preprint version.

Comment on a paper of Ashtekar and Isham. Class. Quantum Grav. 10:605-608 (1993).

(with T. Baumgarte) Regularity of spherically symmetric static solutions of the Einstein equations. Class. Quantum Grav. 10:327-332 (1993).

(with G. Rein) Smooth static solutions of the spherically symmetric Vlasov-Einstein system. Ann. Inst. H. Poincaré (Physique Theorique) 59:383-397 (1993).

(with G. Rein) The Newtonian limit of the spherically symmetric Vlasov-Einstein system. Commun. Math. Phys. 150:585-591 (1992).

(with G. Rein) Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data. Commun. Math. Phys. 150:561-583 (1992).

On the choice of matter model in general relativity. In R. d'Inverno (ed.) Approaches to Numerical Relativity (Cambridge University Press: Cambridge 1992).

On the definition of post-Newtonian approximations. Proc. R. Soc. Lond. 438:341-360 (1992).

Cosmic censorship and the Vlasov equation. Class. Quantum Grav. 9:L99-L104 (1992).

The initial value problem for self-gravitating fluid bodies. In K. Schmüdgen (ed.) Mathematical Physics X (Springer: Berlin 1992).

The initial value problem for a class of general relativistic fluid bodies. J. Math. Phys. 33:1047-1053 (1992).

The characteristic initial value problem for the Einstein equations. In Murthy, M.K.V. and Spagnolo, S. Nonlinear Hyperbolic Equations and Field Theory (Pitman:London 1992).

(with B.G.Schmidt) Existence and properties of spherically symmetric static fluid bodies with given equation of state. Class. Quantum Grav. 8:985-1000 (1991).

Stability in the characteristic initial value problem. In Z. Perjes (ed.) Relativity Today (Nova:New York 1991).

Convergent and divergent perturbation series and the post-Minkowskian approximation scheme. Class. Quantum Grav. 7:803-812 (1990).

Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations. Proc. R. Soc. Lond. A 427:221-239 (1990).

(with G.S.Hall) Local and global algebraic structures in general relativity. Int. J. Theor. Phys. 28:365-375 (1989).

(with G.S.Hall and W.Kay) The curvature problem in general relativity. Gen. Rel. Grav. 21:439-446 (1989).

Describing spacetimes by their curvature. In R. Bartnik (ed.) Proc. Centre Math. Anal., Australian National University, 19 (1989).

Insufficiency of the Bianchi and Ricci identities for characterising curvature. J. Geom. Phys. 6:159-163 (1989).

The Robinson-Trautman equation and Lyapunov functions. In D.G. Blair , M.J. Buckingham (eds.) Proc. 5th Marcel Grossman Meeting, Part A (1989).

Existence and asymptotic properties of global solutions of the Robinson-Trautman equation. Class. Quantum Grav. 5:1339-1347 (1988).

The continuous determination of space-time geometry by the Riemann curvature tensor. Class. Quantum Grav. 5:695-705 (1988).

Curvature of generic space-times in general relativity. J. Math. Phys. 29:1569-1574 (1988).

(with G.S.Hall) Uniqueness of the metric from the Weyl and energy-momentum tensors. J. Math. Phys. 28:1837-1839 (1987).

(with G.S.Hall) Sectional curvature in general relativity. Gen. Rel. Grav. 19:771-789 (1987).