Semilinear partial differential equations
Monte-Carlo Algorithms for Forward Feynman-Kac type representation for semilinear nonconservative Partial Differential Equations
... September 11th 2017 Abstract The paper is devoted to the construction of a probabilistic particle algorithm. This is related to nonlin- ear forward Feynman-Kac type equation, which represents the solution of a ...
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Shape optimization of a Dirichlet type energy for semilinear elliptic partial differential equations
... gu Ω . In this article, we introduce and investigate a prototypal problem close to the standard “Dirichlet energy shape minimization”, involving a nonlinear differential operator. The questions we wish to study ...
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Forward Feynman-Kac type representation for semilinear nonconservative Partial Differential Equations
... Burgers-Fisher equations which are of great importance to represent nonlinear phenomena in various fields such as bi- ology [1, 27], physiology [19] and physics ...These equations have the particular ...
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Shape optimization of a Dirichlet type energy for semilinear elliptic partial differential equations
... . In this article, we introduce and investigate a prototypal problem close to the standard “Dirichlet energy shape minimization”, involving a nonlinear differential operator. The questions we wish to study here ...
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Sharp Derivative Bounds for Solutions of Degenerate Semi-Linear Partial Differential Equations
... X i=1 V i 2 u(t, x) + V 0 u(t, x) + f t, x, u(t, x), ( ∇ x u(t, x)) ⊤ , (t, x) ∈ (0, ∞) × R d , where ∇ x u is the usual gradient of u in x, i.e., the row vector of partial derivatives (∂ x 1 u, . . . , ∂ x N u). ...
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Nonlinear damped partial differential equations and their uniform discretizations
... such equations, see ...of equations of interest, not covered by our main result, is the stability of semilinear wave equations with locally distributed ...
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Accelerated finite elements schemes for parabolic stochastic partial differential equations
... Stochastic Partial Differential Equations driven by Poisson Random Measures of Jump Type, SIAM ...for semilinear parabolic stochastic equations with additive noise, ...
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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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Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case
... In the case of hyperbolic conservation laws [ 7 ], the authors defined a notion of generalized kinetic solution and obtained a comparison result showing that any generalized kinetic solution is actually a kinetic ...
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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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Probabilistic representation of a class of non conservative nonlinear Partial Differential Equations
... [12] I. Karatzas and S. E. Shreve. Brownian motion and stochastic calculus, volume 113 of Graduate Texts in Mathematics. Springer-Verlag, New York, second edition, 1991. [13] A. Le Cavil, N. Oudjane, and F. Russo. ...
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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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Normalized solutions to strongly indefinite semilinear equations
... elliptic partial differential equations, Morse index, indefinite functionals, varia- tional methods, ...indefinite semilinear elliptic equations in un- bounded domains has been a long ...
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Novel 4-D Algorithm for Functional MRI Image Regularization using Partial Differential Equations
... Synopsis State-of-the-art techniques for denoising functional MRI (fMRI) im- ages consider the problems of spatial and temporal regularization as decoupled tasks. In this work we propose a partial ...
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McKean Feynman-Kac probabilistic representations of non-linear partial differential equations
... 2. In the second approach we recall that v is viewed as the solution of (7.6). The problem amounts then to discretize a non-linear PDE. Then one can rely on numerical analysis methods (e.g. finite differences, or finite ...
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Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
... , ∀k ∈ K. Our goal is the development of numerical methods that permit the rapid yet accurate and reliable prediction of these PDE-induced input-output relationships in real-time or in the limit of many queries — ...
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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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Optimal control of partial differential equations based on the Variational Iteration Method
... linear partial differential ...Hamilton–Pontryagin equations. These linear partial differential equations constitute a multi-point-boundary value ...Hamilton–Pontryagin ...
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Partial differential matrix equations for the inverse problem of scattering theory
... Redistribution subject to AIP license or copyright, see http://jmp.aip.org/jmp/copyright.jsp... Redistribution subject to AIP license or copyright, see http://jmp.aip.org/jmp/copyright.j[r] ...
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Mixing Monte-Carlo and Partial Differential Equations for Pricing Options
... The methods are based on a combination of Monte-Carlo, quadrature and partial differential equations or PDE for short methods.. The key idea was studied by two of the authors a few years [r] ...
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