Results 21 to 30 of about 14,089 (117)
, 2010 Exotic heat equations that allow to prove the Poincar\'e conjecture, some related problems and suitable generalizations too are considered. The methodology used is the PDE's algebraic topology, introduced by A.
Prástaro, Agostino
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Communications on Pure and Applied Mathematics, EarlyView.Abstract We address the problem of regularity of solutions ui(t,x1,…,xN)$u^i(t, x^1, \ldots, x^N)$ to a family of semilinear parabolic systems of N$N$ equations, which describe closed‐loop equilibria of some N$N$‐player differential games with Lagrangian having quadratic behaviour in the velocity variable, running costs fi(x)$f^i(x)$ and final costs gi(
Marco Cirant, Davide Francesco Redaelli
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Randomly sparsified Richardson iteration: A dimension‐independent sparse linear solver
Communications on Pure and Applied Mathematics, EarlyView.Abstract Recently, a class of algorithms combining classical fixed‐point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as 10108×10108$10^{108} \times 10^{108}$. So far, a complete mathematical explanation for this success has proven elusive.
Jonathan Weare, Robert J. Webber
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Global and microlocal aspects of Dirac operators: Propagators and Hadamard states
Mathematische Nachrichten, EarlyView.Abstract We propose a geometric approach to construct the Cauchy evolution operator for the Lorentzian Dirac operator on Cauchy‐compact globally hyperbolic 4‐manifolds. We realize the Cauchy evolution operator as the sum of two invariantly defined oscillatory integrals—the positive and negative Dirac propagators—global in space and in time, with ...
Matteo Capoferri, Simone Murro
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We analyze nonlinear degenerate coupled partial differential equation (PDE)‐PDE and PDE‐ordinary differential equation (ODE) systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular diffusion.
K. Mitra, S. Sonner
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT The paper proposes a variational analysis of the 1‐hypergeometric stochastic volatility model for pricing European options. The methodology involves the derivation of estimates of the weak solution in a weighted Sobolev space. The weight is closely related to the stochastic volatility dynamic of the model.
José Da Fonseca, Wenjun Zhang
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BSDEs with terminal conditions that have bounded Malliavin derivative
, 2013 We show existence and uniqueness of solutions to BSDEs of the form $$ Y_t = \xi + \int_t^T f(s,Y_s,Z_s)ds - \int_t^T Z_s dW_s$$ in the case where the terminal condition $\xi$ has bounded Malliavin derivative.
Cheridito, Patrick, Nam, Kihun
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Optimal Control Applications and Methods, EarlyView.Optimal adaptive reinforcement learning control using an actor‐critic architecture. The controller learns optimal control policies online from data measured along the trajectories of a plug flow system ABSTRACT This article is devoted to optimal adaptive control for a distributed parameter convection‐reaction system by reinforcement learning (RL ...
Abdellaziz Binid, Ilyasse Aksikas
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A Physics‐Informed Learning Framework to Solve the Infinite‐Horizon Optimal Control Problem
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT We propose a physics‐informed neural networks (PINNs) framework to solve the infinite‐horizon optimal control problem of nonlinear systems. In particular, since PINNs are generally able to solve a class of partial differential equations (PDEs), they can be employed to learn the value function of the infinite‐horizon optimal control problem via
Filippos Fotiadis +1 more
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Fractional Cauchy problems on bounded domains
, 2008 Fractional Cauchy problems replace the usual first-order time derivative by a fractional derivative. This paper develops classical solutions and stochastic analogues for fractional Cauchy problems in a bounded domain $D\subset\mathbb{R}^d$ with Dirichlet
Meerschaert, Mark M. +2 more
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