Christopher Henderson
 Associate Professor, Mathematics
 Member of the Graduate Faculty
Contact
 (520) 6216892
 Mathematics, Rm. 601
 Tucson, AZ 85721
 ckhenderson@arizona.edu
Degrees
 Ph.D. Mathematics
 Stanford University, Stanford, California, United States
 Propagation Phenomena in ReactionAdvectionDiffusion Equations
 B.S. Mathematics
 University of Chicago, Chicago, Illinois, United States
Work Experience
 University of Chicago (2016  2019)
 Ecole Normale Superieure de Lyon (2015  2016)
Awards
 College of Science Distinguished EarlyCareer Teaching Award (nominated, not awarded)
 Spring 2023
 Excellence in Postdoctoral Mentoring Award (nominated, not awarded)
 University of Arizona, Fall 2022
Interests
Teaching
Mathematical analysis, applied math
Research
Mathematical analysis, applied mathematics, partial differential equations, mathematical physics, mathematical biology, probability, reactiondiffusion equations, kinetic equations
Courses
202425 Courses

APPL Research
APPL 900 (Fall 2024) 
Theoretical Found AppMth I
APPL 584A (Fall 2024) 
Theoretical Found AppMth I
MATH 584A (Fall 2024)
202324 Courses

Independent Study
MATH 599 (Spring 2024) 
Theoretical Found AppMth II
MATH 584B (Spring 2024) 
Theoretical Found AppMth I
APPL 584A (Fall 2023) 
Theoretical Found AppMth I
MATH 584A (Fall 2023) 
Topics Modern Analysis
MATH 529 (Fall 2023)
202223 Courses

Calculus II
MATH 129 (Spring 2023) 
Theoretical Found AppMth II
MATH 584B (Spring 2023) 
Thesis
MATH 910 (Spring 2023) 
Calculus II
MATH 129 (Fall 2022) 
Independent Study
MATH 599 (Fall 2022) 
Theoretical Found AppMth I
APPL 584A (Fall 2022) 
Theoretical Found AppMth I
MATH 584A (Fall 2022) 
Thesis
MATH 910 (Fall 2022)
202122 Courses

Independent Study
MATH 599 (Spring 2022) 
Adv Applied Mathematics
MATH 422 (Fall 2021) 
Adv Applied Mathematics
MATH 522 (Fall 2021) 
Independent Study
MATH 599 (Fall 2021)
202021 Courses

Independent Study
MATH 599 (Spring 2021) 
Independent Study
MATH 599 (Fall 2020) 
Math of BioSystems
MATH 119A (Fall 2020)
201920 Courses

Anls Ord Diff Equations
MATH 355 (Spring 2020) 
Calculus I
MATH 125 (Fall 2019)
Scholarly Contributions
Journals/Publications
 Gu, Y., & Henderson, C. (2023). Longtime behaviour for a nonlocal model from directed polymers. Nonlinearity, 36(2), 902954.
 Henderson, C., & Wang, W. (2023). Kinetic Schauder estimates with timeirregular coefficients and uniqueness for the Landau equation.More infoWe prove a Schauder estimate for kinetic FokkerPlanck equations thatrequires only H\"older regularity in space and velocity but not in time. As anapplication, we deduce a weakstrong uniqueness result of classical solutionsto the spatially inhomogeneous Landau equation beginning from initial datahaving H\"older regularity in $x$ and only a logarithmic modulus of continuityin $v$. This replaces an earlier result requiring H\"older continuity in bothvariables.[Journal_ref: ]
 An, J., Henderson, C., & Ryzhik, L. (2022). Quantitative steepness, semiFKPP reactions, and pushmipullyu fronts.More infoWe uncover a seemingly previously unnoticed algebraic structure of a largeclass of reactiondiffusion equations and use it, in particular, to study thelong time behavior of the solutions and their convergence to traveling waves inthe pulled and pushed regimes, as well as at the pushmipullyu boundary. Onesuch new object introduced in this paper is the shape defect function, which,indirectly, measures the difference between the profiles of the solution andthe traveling wave. While one can recast the classical notion of `steepness' interms of the positivity of the shape defect function, its positivity can,surprisingly, be used in numerous quantitative ways. In particular, thepositivity is used in a new weighted HopfCole transform and in a relativeentropy approach that play a key role in the stability arguments. The shapedefect function also gives a new connection between reactiondiffusionequations and reaction conservation laws at the pulledpushed transition. Othersimple but seemingly new algebraic constructions in the present paper supplyvarious unexpected inequalities sprinkled throughout the paper. Of note is anew variational formulation that applies equally to pulled and pushed fronts,opening the door to an asyetelusive variational analysis in the pulled case.[Journal_ref: ]
 An, J., Henderson, C., & Ryzhik, L. (2022). Voting models and semilinear parabolic equations. arxiv.More infoWe present probabilistic interpretations of solutions to semilinear parabolic equations with polynomial nonlinearities in terms of the voting models on the genealogical trees of branching Brownian motion (BBM). These extend the connection between the FisherKPP equation and BBM discovered by McKean in~\cite{McK}. In particular, we present ``random outcome'' and ``random threshold'' voting models that yield any polynomial nonlinearity $f$ satisfying $f(0)=f(1)=0$ and a ``recursive up the tree'' model that allows to go beyond this restriction on $f$. We compute a few examples of particular interest; for example, we obtain a curious interpretation of the heat equation in terms of a nontrivial voting model and a ``groupbased'' voting rule that leads to a probabilistic view of the pushmipullyu transition for a class of nonlinearities introduced by Ebert and van Saarloos. [Journal_ref: ]
 Calvez, V., Henderson, C., Mirrahimi, S., Turanova, O., & Dumont, T. (2022). Nonlocal competition slows down front acceleration during dispersal evolution. Ann. H. Lebesgue, 5, 171.
 Griette, Q., Henderson, C., & Turanova, O. (2022). Speedup of traveling waves by negative chemotaxis. arxiv.More infoWe consider the traveling wave speed for FisherKPP (FKPP) fronts under the influence of repulsive chemotaxis and provide an almost complete picture of its asymptotic dependence on parameters representing the strength and lengthscale of chemotaxis. Our study is based on the convergence to the porous medium FKPP traveling wave and a hyperbolic FKPPKellerSegel traveling wave in certain asymptotic regimes. In this way, it clarifies the relationship between three equations that have each garnered intense interest on their own. Our proofs involve a variety of techniques ranging from entropy methods and decay of oscillations estimates to a general description of the qualitative behavior to the hyperbolic FKPPKellerSegel equation. For this latter equation, we, as a part of our limiting arguments, establish an explicit lower bound on the minimal traveling wave speed and provide a new construction of traveling waves that extends the known existence range to all parameter values. [Journal_ref: ]
 Henderson, C. (2022). Slow and fast minimal speed traveling waves of the FKPP equation with chemotaxis. J. Math. Pures Appl. (9), 167, 175203.
 Henderson, C., & Wang, W. (2022). Local wellposedness for the Boltzmann equation with very soft potential and polynomially decaying initial data. SIAM J. Math. Anal., 54(3), 28452875.
 Henderson, C., Snelson, S., & Tarfulea, A. (2022). Classical solutions of the Boltzmann equation with irregular initial data.More infoThis article considers the spatially inhomogeneous, noncutoff Boltzmannequation. We construct a largedata classical solution given bounded,measurable initial data with uniform polynomial decay of mild order in thevelocity variable. Our result requires no assumption of strict positivity forthe initial data, except locally in some small ball in phase space. We alsoobtain existence results for weak solutions when our decay and positivityassumptions for the initial data are relaxed. Because the regularity of oursolutions may degenerate as $t \rightarrow 0$, uniqueness is a challengingissue. We establish weakstrong uniqueness under the additional assumption thatthe initial data possesses no vacuum regions and is H\"older continuous. As anapplication of our shorttime existence theorem, we prove global existence nearequilibrium for bounded, measurable initial data that decays at a finitepolynomial rate in velocity.[Journal_ref: ]
 An, J., Henderson, C., & Ryzhik, L. (2021). Pushed, pulled and pushmipullyu fronts of the BurgersFKPP equation. arXiv preprint arXiv:2108.07861, accepted Journal of the European Mathematical Society.
 Bouin, E., & Henderson, C. (2021). The Bramson delay in a FisherKPP equation with logsingular nonlinearity. Nonlinear Anal., 213, Paper No. 112508, 30.
 Bramburger, J. J., & Henderson, C. (2021). The speed of traveling waves in a FKPPBurgers system. Arch. Ration. Mech. Anal., 241(2), 643681.
 Gu, Y. u., & Henderson, C. (2021). A PDE hierarchy for directed polymers in random environments. Nonlinearity, 34(10), 73357370.
 Henderson, C. (2020). Local wellposedness of the Boltzmann equation with polynomially decaying initial data. Kinetic and Related Models. doi:http://dx.doi.org.ezproxy1.library.arizona.edu/10.3934/krm.2020029More infoWe consider the Cauchy problem for the spatially inhomogeneous noncutoffBoltzmann equation with polynomially decaying initial data in the velocityvariable. We establish shorttime existence for any initial data with thisdecay in a fifth order Sobolev space by working in a mixed $L^2$ and $L^\infty$space that allows to compensate for potential moment generation and obtainingnew estimates on the collision operator that are welladapted to this space.Our results improve the range of parameters for which the Boltzmann equation iswellposed in this decay regime, as well as relax the restrictions on theinitial regularity. As an application, we can combine our existence result withthe recent conditional regularity estimates of ImbertSilvestre(arXiv:1909.12729 [math.AP]) to conclude solutions can be continued for as longas the mass, energy, and entropy densities remain under control. Thiscontinuation criterion was previously only available in the restricted range ofparameters of previous wellposedness results for polynomially decaying initialdata.[Journal_ref: ]
 Henderson, C. (2020). Selfgenerating lower bounds and continuation for the Boltzmann equation. Calculus of Variations and Partial Differential Equations.More infoFor the spatially inhomogeneous, noncutoff Boltzmann equation posed in thewhole space $\mathbb R^3_x$, we establish pointwise lower bounds that appearinstantaneously even if the initial data contains vacuum regions. Our lowerbounds depend only on the initial data and upper bounds for the mass and energydensities of the solution. As an application, we improve the weakest knowncontinuation criterion for largedata solutions, by removing the assumptions ofmass bounded below and entropy bounded above.[Journal_ref: ]
 Henderson, C., & Souganidis, P. E. (2020). Brownian fluctuations of flame fronts with small random advection. Mathematical Models and Methods in Applied Sciences, 30(07), 13751406. doi:10.1142/s0218202520500256
 Henderson, C., Bouin, E., & Ryzhik, L. (2020). The Bramson delay in the nonlocal FisherKPP equation. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 37(1), 5177. doi:10.1016/j.anihpc.2019.07.001
 Henderson, C., Snelson, S., & Tarfulea, A. (2020). Local solutions of the Landau equation with rough, slowly decaying initial data. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 37(6), 13451377. doi:10.1016/j.anihpc.2020.04.004
 Hamel, F., & Henderson, C. (2019). Propagation in a FisherKPP equation with nonlocal advection. Journal of Functional Analysis, 108426.
 Henderson, C., & Snelson, S. (2019). C\^{}â Smoothing for Weak Solutions of the Inhomogeneous Landau Equation. Arch. Ration. Mech. Anal., 151.
 Henderson, C., Snelson, S., & Tarfulea, A. (2019). Local existence, lower mass bounds, and a new continuation criterion for the Landau equation. Journal of Differential Equations, 266(23), 15361577.
 Henderson, C., Snelson, S., & Tarfulea, A. (2020). Local Solutions of the Landau Equation with Rough, Slowly Decaying Initial Data. Annales de l'Institut Henri Poincaré C, Analyse non linéaire. doi:https://doiorg.ezproxy1.library.arizona.edu/10.1016/j.anihpc.2020.04.004
Proceedings Publications
 Bouin, E., Henderson, C., & Ryzhik, L. (2019). The Bramson delay in the nonlocal FisherKPP equation. In Annales de l'Institut Henri Poincar\'e C, Analyse non lin\'eaire.