Results 31 to 40 of about 822,876 (350)
Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport [PDF]
Physical Review Research, 2022 Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning.
Lu Lu +3 more
semanticscholar +1 more source
Advances in Difference Equations, 2020 On this paper, for an arbitrary order operator-differential equation with the weight e − α t 2 , α ∈ ( − ∞ , + ∞ ) $e^{\frac{-\alpha t}{2}}, \alpha \in (-\infty ,+ \infty )$ , in the space W 2 n + m ( R + ; H ) $W^{n+m}_{2}(R_{+};H)$ , we attain ...
Nashat Faried +2 more
doaj +1 more source
Deterministic numerical solutions of the Boltzmann equation using the fast spectral method [PDF]
, 2013 The Boltzmann equation describes the dynamics of rarefied gas flows, but the multidimensional nature of its collision operator poses a real challenge for its numerical solution. In this paper, the fast spectral method [36], originally developed by Mouhot
Reese, Jason M. +6 more
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Neutral Operator and Neutral Differential Equation
Abstract and Applied Analysis, 2011 In this paper, we discuss the properties of the neutral operator (Ax)(t)=x(t)−cx(t−δ(t)), and by applying coincidence degree theory and fixed point index theory, we obtain sufficient conditions for the existence, multiplicity, and nonexistence of ...
Jingli Ren, Zhibo Cheng, Stefan Siegmund
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Indefinite Hamiltonian systems whose Titchmarsh–Weyl coefficients have no finite generalized poles of non-positive type [PDF]
, 2013 The two-dimensional Hamiltonian system (*) y'(x)=zJH(x)y(x), x∈(a,b), where the Hamiltonian H takes non-negative 2x2-matrices as values, and $J:= \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$, has attracted a lot of interest over the past decades ...
Harald Woracek +3 more
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Initial boundary value problems for a fractional differential equation with hyper-Bessel operator [PDF]
, 2016 Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart of a hyper-Bessel differential operator are considered.
F. Al-Musalhi, N. Al-Salti, E. Karimov
semanticscholar +1 more source
Optimal control of an abstract evolution variational inequality with application to homogenized plasticity [PDF]
Journal of Nonsmooth Analysis and Optimization, 2020 The paper is concerned with an optimal control problem governed by a state equation in form of a generalized abstract operator differential equation involving a maximal monotone operator.
Hannes Meinlschmidt +2 more
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Complexity, 2021 In this paper, the variational inequality with constraints can be viewed as an optimization problem. Using Lagrange function and projection operator, the equivalent operator equations for the variational inequality with constraints under the certain ...
Li Wang, Xingxu Chen, Juhe Sun
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On Multidimensional Determinant Differential-Operator Equations
Владикавказский математический журнал, 2020 Рассмотрен класс многомерных детерминантных дифференциально-операторныхnуравнений, левая часть которых представляет собой определитель с элементами, содержащими произведение линейных одномерных дифференциальных операторов произвольного порядка, а правая часть зависит от искомой функции и ее первых производных.
openaire +1 more source
Hyperbolic differential‐operator equations on a whole axis [PDF]
Abstract and Applied Analysis, 2004 We give an abstract interpretation of initial boundary value problems for hyperbolic equations such that a part of initial boundary value conditions contains also a differentiation on the time t of the same order as equations. The case of stable solutions of abstract hyperbolic equations is treated.
openaire +4 more sources