Results 151 to 160 of about 1,352,769 (228)

Besov Spaces of Self-affine Lattice Tilings and Pointwise regularity(Harmonic Analysis and Nonlinear Partial Differential Equations)

, 2006
Kōichi Saka
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Quantum Simulation of Partial Differential Equations via Schrödingerization.

Physical Review Letters, 2022
We present a novel new way-called Schrödingerization-to simulate general (quantum and nonquantum) systems of linear ordinary and partial differential equations (PDEs) via quantum simulation.
Shi Jin, Nana Liu, Yue Yu
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Quantum simulation of partial differential equations: Applications and detailed analysis

Physical Review A, 2022
We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation.
Shi Jin, Nana Liu, Yue Yu
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Pseudoparabolic Partial Differential Equations

SIAM Journal on Mathematical Analysis, 1970
This is the publisher’s final pdf. The published article is copyrighted by the Society for Industrial and Applied Mathematics and can be found at: http://epubs.siam.org/loi/sjmaah.
Showalter, R. E., Ting, T. W.
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Introduction to Partial Differential Equations

, 2020
These notes are based on the course Introduction to Partial Differential Equations that the author held during the Spring Semester 2019 for bachelor and master students in mathematics and physics at ETH. They are not supposed to replace the several books
G. Folland
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Partial Differential Equations and Difference Equations

Proceedings of the American Mathematical Society, 1965
(1. 1) Pi(alax)y = ? (1 _ i _ m) where x = (x1, * , xn), a/ax = (a/ax1, *, O/0xn). The Pi's are assumed to be homogeneous polynomials with real coefficients. The term solution is used to include the generalized solutions. A generalized solution is any function continuous on R which is a uniform limit on compact subsets of CX solutions (see [2, p. 65]).
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ON STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Mathematics of the USSR-Sbornik, 1975
In this paper we consider the Cauchy problem for second-order stochastic partial differential equations of parabolic type. We study linear and nonlinear equations for filtering Markov diffusion processes. Theorems on the existence, uniqueness and smoothness of solutions are proved.Bibliography: 21 items.
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Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

Communications in Mathematics and Statistics, 2017
We study a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, which is based on an analogy between the BSDE and reinforcement learning with the gradient of ...
Weinan E, Jiequn Han, Arnulf Jentzen
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On Hyperbolic Partial Differential Equations

American Journal of Mathematics, 1952
where p = zx, q = zy, it is assumed that f is continuous in (x, y, z, p, q) and satisfies a uniform Lipschitz conditioni with respect to (z, p, q). It will be shown (Section 2) that the assumption of a Lipschitz. condition with respect to z can be omitted in these existence theorems, though not in the uniqueness theorems.
Hartman, Philip, Wintner, Aurel
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