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Tournus Magali (École Centrale de Marseille)  OskarMorgensternPlatz 1, Hörsaal 2, ground floor.  Thu, 23. Nov 17, 14:15 
Scalar conservation laws with heterogeneous flux in the BV framework  
We consider a scalar conservation law with a flux containing spatial heterogeneities of bounded variation, where the number of discontinuities may be infinite. We address the question of existence of an adapted entropy solution in the BV framework. A sufficient key condition guaranteeing existence is identified and new BV estimates are given. This provides the most general BV theory available. Moreover, we show with a counterexample that if this hypothesis is violated, the problem may be illposed in the BV framework.  

Fellner Klemens (University of Graz)  WPI, OMP 1, Seminar Room 08.135  Fri, 24. Mar 17, 15:10 
Regularity and Equilibration for spatially inhomogeneous coagulationfragmentation models  
We consider results on discrete and continuous coagulation and coagulationfragmentation models. For discrete models, we shall present some recent regularity results concerning smoothness of moments and absence of gelation. For the continuous Smoluchowski equation with constant rates, we shall prove exponential, resp. superlinear convergence to equlibrium. This are joint works with M. Breden, J.A. Canizo, J.A. Carrillo and L. Desvillettes.  

Cańizo José A. (University of Granada, Spain)  WPI, OMP 1, Seminar Room 08.135  Fri, 24. Mar 17, 14:30 
Asymptotic behaviour of the BeckerDöring equations  
We will present some recent results on the long behaviour of the BeckerDöring equations, mainly involving subcritical solutions: speed of convergence to equilibrium (sometimes exponential, sometimes algebraic) and some new uniform bounds on moments. We will also comment on a continuous model that serves as an analogy of the discrete equations, that seems to exhibit a similar longtime behaviour. This talk is based on collaborations with J. Conlon, A. Einav, B. Lods and A. Schlichting.  

Salort Delphine (University Pierre & Marie Curie, Paris, France)  WPI, OMP 1, Seminar Room 08.135  Fri, 24. Mar 17, 11:40 
Fragmentation Equations and FokkerPlanck equations in neuroscience  
In this talk, we present two types of linked partial differential equation models that describe the evolution of an interacting neural network and where neurons interact with one another through their common statistical distribution. We will show, according to the choice of EDP studied, what information can be obtained in terms of synchronization phenomena, qualitative and asymptotic properties of these solutions and what are the specific difficulties on each of these models.  

Banasiak Jacek (University of Pretoria, South Africa)  WPI, OMP 1, Seminar Room 08.135  Fri, 24. Mar 17, 11:10 
Analytic fragmentation semigroups and discrete coagulationfragmentation processes with growth  
In the talk we shall describe how the substochastic semigroup theory can be used to prove analyticity of a class of fragmentation semigroup. This result is applied to discrete fragmentation processes with growth to analyze their long time behaviour and to prove the existence of classical solutions to equations describing such processes combined with coagulation.  

Laurençot Philippe (Institut de Mathématiques de Toulouse, France)  WPI, OMP 1, Seminar Room 08.135  Fri, 24. Mar 17, 10:10 
Selfsimilar solutions to coagulationfragmentation equations  
When the coagulation kernel and the overall fragmentation rate are homogeneous of degree ë and ă > 0, respectively, there is a critical value ëc := ă + 1 which separates two different behaviours: all solutions are expected to be massconserving when ë < ëc while gelation is expected to take place when ë > ëc, provided the mass of the initial condition is large enough. The focus of this talk is the case ë = ëc for which we establish the existence of massconserving selfsimilar solutions. This is partly a joint work with Henry van Roessel (Edmonton).  

Niethammer Barbara (Institut for applied mathematics, Bonn, Germany)  WPI, OMP 1, Seminar Room 08.135  Fri, 24. Mar 17, 9:30 
The coagulation equation: kernels with homogeneity one  
The question whether the longtime behaviour of solutions to Smoluchowski's coagulation equation is characterized by selfsimilar solutions has received a lot of interest within the last two decades. While this issue is by now wellunderstood for the three solvable cases, the theory for nonsolvable kernels is much less developed. For kernels with homogeneity smaller than one existence results for selfsimilar solutions and some partial uniqueness results are available. In this talk I will report on some recent results on the borderline case of kernels with homogeneity of degree one. For socalled class II kernels we can prove the existence of a family of selfsimilar solutions. For class I, or diagonally dominant, kernels, it is known that selfsimilar solutions cannot exist. Formal arguments suggest that the longtime behaviour of solutions is, in suitable variables, to leading order the same as for the Burgers equation. However, in contrast to diffusive regularizations, we obtain phenomena such as instability of the constant solution or oscillatory traveling waves. (Joint work with Marco Bonacini, Michael Herrmann and Juan Velazquez)  

Gwiazda Piotr (Polish academy of sciences, Poland)  WPI, OMP 1, Seminar Room 08.135  Thu, 23. Mar 17, 16:40 
Relative entropy method for measure solutions in mathematical biology  
In the last years there has appeared several applications of relative entropy method for strong measurevalued uniqueness of solutions in physical models (see: e.g. incompressible Euler equation [1], polyconvex elastodynamics [2], compressible Euler equation [3], compressible NavierStokes equation [4]). The topic of the talk will be application of similar techniques to structured population models. Preliminary result in this direction was obtain in [5]. The talk is based on the joint result with Marie DoumicJauffret and Emil Wiedemann. [1] Y. Brenier, C. De Lellis, and L. Sz´ekelyhidi, Jr. Weakstrong uniqueness for measurevalued solutions. Comm. Math. Phys., 305(2):351361, 2011. [2] S. Demoulini, D.M.A. Stuart, and A.E. Tzavaras. Weakstrong uniqueness of dissipative measurevalued solutions for polyconvex elastodynamics. Arch. Ration. Mech. Anal., 205(3):927961, 2012. [3] P. Gwiazda, A. wierczewskaGwiazda, and E. Wiedemann. Weakstrong uniqueness for measurevalued solutions of some compressible fluid models. Nonlinearity, 28(11):38733890, 2015. [4] E. Feireisl, P. Gwiazda, A. wierczewskaGwiazda and E. Wiedemann Dissipative measurevalued solutions to the compressible NavierStokes system, Calc. Var. Partial Differential Equations 55 (2016), no. 6, 55141 [5] P. Gwiazda, E. Wiedemann, Generalized Entropy Method for the Renewal Equation with Measure Data, to appear in Commun. Math. Sci., arXiv:1604.07657  

Van Brunt Bruce (Massey university, New Zealand)  WPI, OMP 1, Seminar Room 08.135  Thu, 23. Mar 17, 16:00 
Analytic solutions to certain equations from a cell division equation  
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Haas Bénédicte (University of Paris XIII, France)  WPI, OMP 1, Seminar Room 08.135  Thu, 23. Mar 17, 14:40 
The fragmentation equation with shattering  
We consider fragmentation equations with nonconservative solutions, some mass being lost to a dust of zeromass particles as a consequence of an intensive splitting. Under assumptions of regular variation on the fragmentation rate, we describe the large time behavior of solutions. Our approach is based on probabilistic tools: the solutions to the fragmentation equations are constructed via nonincreasing selfsimilar Markov processes that continuously reach 0 in finite time. We describe the asymptotic behavior of these processes conditioned on nonextinction and then deduced the asymptotics of solutions to the equation.  

Bertoin Jean (University of Zürich, Switzerland)  WPI, OMP 1, Seminar Room 08.135  Thu, 23. Mar 17, 14:00 
A probabilistic approach to spectral analysis of growthfragmentation equations (based on a joint work with Alex Watson, Manchester University)  
The growthfragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach to the study of this asymptotic behaviour. We use a FeynmanKac formula to relate the solution of the growthfragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the spectral radius and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growthfragmentation operator and its dual. In special cases, we obtain exponential convergence.  

Gabriel Pierre (University of VersaillesSaintQuentin, France)  WPI, OMP 1, Seminar Room 08.135  Thu, 23. Mar 17, 11:10 
Long time behaviour of growthfragmentation equations  
Growthfragmentation equations can exhibit various asymptotic behaviours. In this talk we illustrate this diversity by working in suitable weighted L^p spaces which are associated to entropy functionals. We prove that, depending on the choice of the coefficients, the following behaviours can happen: uniform exponential convergence to the equilibrium, nonuniform convergence to the equilibrium, or convergence to periodic solutions. This is a joint work with Etienne Bernard and Marie Doumic.  

Mischler Stéphane (University ParisDauphine, France)  WPI, OMP 1, Seminar Room 08.135  Thu, 23. Mar 17, 10:30 
Long time asymptotic of the solutions to the growthfragmentation equation  
I will discuss the long time asymptotic of the solutions to the growthfragmentation equation, presenting several results and approaches. I will then focus on the spectral analysis and semigroup approach for which I will give some more details about the proof.  

Buszkowski Wojciech (Adam Mickiewicz University)  WPI, OMP 1, Seminar Room 08.135  Wed, 15. Mar 17, 10:00 
Some open problems in substructural logics  
I will focus on several substructural logics, mainly conservative extensions of the Lambek calculus (associative and nonassociative, with and without constants) and point out some basic open problems. Examples: the lower bound of the complexity of the full nonassociative Lambek calculus, the decidability of Pratt's action logic, the decidability of the consequence relation for the nonassociative Lambek calculus with involutive negations, the decidability of the equational theory of latticeordered pregroups. I will briefly discuss what is known in these areas.  

Brotherston James (University College London)  WPI, OMP 1, Seminar Room 08.135  Tue, 14. Mar 17, 10:00 
Biabduction (and Related Problems) in Array Separation Logic  
I describe array separation logic (ASL), a variant of separation logic in which the data structures are either pointers or arrays. This logic can be used, e.g., to give memory safety proofs of imperative array programs. The key to automatically inferring specifications is the socalled "biabduction" problem, given formulas A and B, find formulas X and Y such that A + X = B + Y (and such that A + X is also satisfiable), where + is the wellknown "separating conjunction" of separation logic. We give an NP decision procedure for this problem that produces solutions of reasonable quality, and we also show that the problem of finding a consistent solution is NPhard. Along the way, we study satisfiability and entailment in our logic, giving decision procedures and complexity bounds for both problems. This is joint work with Nikos Gorogiannis (Middlesex) and Max Kanovich (UCL).  

Zhang Yong (WPI c/o Courant & NJIT)  WPI, OMP 1, Seminar Room 08.135  Wed, 8. Mar 17, 13:45 
Analysisbased fast algorithms for convolutiontype nonlocal potential in Nonlinear Schrödinger equation  
Convolutiontype potential are common and important in many science and engineering fields. Efficient and accurate evaluation of such nonlocal potentials are essential in practical simulations.In this talk, I will focus on those arising from quantum physics/chemistry and lightningshield protection, including Coulomb, dipolar and Yukawa potentials that are generated by isotropic and anisotropic smooth and fastdecaying density. The convolution kernel is usually singular or discontinuous at the origin and/or at the far field, and density might be anisotropic, which together present great challenges for numerics in both accuracy and efficiency. The stateofart fast algorithms include Wavelet based Method(WavM), kernel truncation method(KTM), NonUniformFFT based method(NUFFT) and GaussianSumbased method(GSM). Gaussiansum/exponentialsum approximation and kernel truncation technique, combined with finite Fourier series and Taylor expansion, finally lead to a O(NlogN) fast algorithm achieving spectral accuracy. Applications to NLSE are reviewed.  

Blanes Sergio (U. Politčcnica de Valčncia)  WPI, OMP 1, Seminar Room 08.135  Tue, 7. Mar 17, 17:15 
Time average on the numerical integration of nonautonomous differential equations  
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Casas Fernando (U. Jaume I Castellón)  WPI, OMP 1, Seminar Room 08.135  Tue, 7. Mar 17, 16:15 
Time dependent perturbation theory in matrix mechanics and time averaging  
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