Parabolic partial differential equations
On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics
... 1 Introduction Many economic problems involve diffusion mechanisms: production factor mobility or technological dissemination are among these phenomena. Other phenomena studied in economics like pollution spreading or ...
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Accelerated finite elements schemes for parabolic stochastic partial differential equations
... stochastic parabolic PDEs of the form of equation ...of equations arise in various fields of sciences and engineering, for example in nonlinear filtering of partially observed diffusion ...these ...
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Bounding of linear output functionals of parabolic partial differential equations
... In the figure, as Ate, the size of the coarse mesh time step, decreases, the resolution of the coarse mesh increases, and the errors drop; eUB is the error in the upp[r] ...
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A Probabilistic Numerical Method for Fully Non-linear Parabolic Partial Differential Equations
... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r] ...
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Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case
... B Y A RNAUD D EBUSSCHE , M ARTINA H OFMANOVÁ AND J ULIEN V OVELLE IRMAR CNRS et ENS Rennes, Max Planck Institute for Mathematics in the Sciences and Université Lyon 1 In this paper, we study the Cauchy problem for a ...
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In-Domain Control of Partial Differential Equations
... elaborated parabolic partial differential equations (PDEs), which involves the effects of both nonlinear propagation and ...Burgers’ equations motivated extensive investigations on the ...
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Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
... and parabolic partial differential equations with affine parameter dependence to problems involving (a) nonaffine dependence on the parameter, and (b) nonlinear dependence on the field ...and ...
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On the Semilinear Parabolic Equations
... This section contains some of our main results. Using semigroup methods we conclude that a quite large class of semilinear parabolic partial differential equations has a unique solution in ...
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Sharp Derivative Bounds for Solutions of Degenerate Semi-Linear Partial Differential Equations
... PARTIAL DIFFERENTIAL EQUATIONS DAN CRISAN AND FRANC ¸ OIS DELARUE A BSTRACT ...degenerate partial differential equations by using probabilistic ...semi-linear parabolic ...
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Stochastic partial differential equations with singular terminal condition
... and the end of the proof will be the same as in the case q > 2. 5 Link with SPDE’s In the introduction, we have said that there is a connection between doubly stochastic backward SDE whose terminal data is a function ...
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On the system of partial differential equations arising in mean field type control
... 10. O. A. Ladyˇ zenskaja, V. A. Solonnikov, and N. N. Ural ′ ceva, Linear and quasilinear equations of parabolic type, Translated from the Russian by S. Smith. Translations of Mathematical Monographs, Vol. ...
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Solving Partial Differential Equations with Chaotic Asynchronous Schemes in Multi- Interaction Systems
... the parabolic equations corresponding to the phenom- ena of diffusion admit well known analytical solutions [22], and can in the same way be solved numerically by various methods (DF, EFF, Monte Carlo ...
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Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations
... December 2017 Abstract. We discuss a class of Backward Stochastic Differential Equations (BSDEs) with no driving martingale. When the randomness of the driver depends on a general Markov process X, those BSDEs are ...
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Nonlinear regularizing effect for hyperbolic partial differential equations
... 1. Motivation Hyperbolic PDEs such as the wave equation are known to propagate singularities, unlike parabolic (or elliptic) PDEs, whose solutions are more regular than the corresponding data. Besides, in the ...
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Certified Reduced Basis Methods for Parametrized Partial Differential Equations
... In this final numerical example, we return to a classic problem, dealing with forced steady heat convection combined with heat conduction in a duct with walls at different temperature and of different lengths. The first ...
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Isogeometric methods for hyperbolic partial differential equations
... I S ogeometric Analysis (IGA) is a generalization of classical FEA. It was first introduced by T.J.R. Hughes, J.A. Cottrell and Y. Bazilevs [43] with the main aim of closing the gap be- tween the geometrical description ...
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An averaging theory for nonlinear partial differential equations
... integrable partial differential equa- tions are usually deduced from idealization of certain physical ...(KdV) equations (which are per- turbations of an integrable PDE) and nonlinear Schrödinger ...
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Optimal control of partial differential equations based on the Variational Iteration Method
... Hamilton–Pontryagin equations are given as a set of coupled linear ...these equations, using the VIM method, an approach is ...co-state equations with unknown parameters that are determined by ...
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Invariant discretizations of partial differential equations
... 4.7. Conclusion To the best of our knowledge, this is the first work attempting to construct invari- ant numerical schemes of differential equations with infinite-dimensional symmetry groups. As our ...
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Applications of probability to partial differential equations and infinite dimensional analysis
... We first review the results in finite dimensional spaces, and then examine the infinite dimensional analog under Gaussian measures.. The various techniques developed [r] ...
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