Mathematics, 2022 This paper proposes a fast meshless scheme for acoustic sensitivity analysis by using the Burton–Miller-type singular boundary method (BM-SBM) and recursive skeletonization factorization (RSF).
Liyuan Lan +5 more
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Three-dimensional fundamental solution in transversely isotropic thermoelastic diffusion material [PDF]
Theoretical and Applied Mechanics, 2012 The aim of the present investigation is to study the fundamental solution for three dimensional problem in transversely isotropic thermoelastic diffusion medium. After applying the dimensionless quantities, two displacement functions are introduced to
Kumar Rajneesh, Chawla Vijay
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Positivity of the fundamental solution for fractional diffusion and wave equations [PDF]
Mathematical methods in the applied sciences, 2019 We study the question of positivity of the fundamental solution for fractional diffusion and wave equations of the form, which may be of fractional order both in space and time.
Jukka Kemppainen
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Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients [PDF]
Manuscripta mathematica, 2016 This paper considers the theory of higher-order divergence-form elliptic differential equations. In particular, we provide new generalizations of several well-known tools from the theory of second-order equations.
Ariel Barton
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Reconstruction of initial heat distribution via Green function method
Electronic Research Archive, 2022 In this paper, layer potential techniques are investigated for solving the thermal diffusion problem. We construct the Green function to get the analytic solution.
Xiaoping Fang +2 more
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Investigation of the Boundary Layers of the Singular Perturbation Problem Including the Cauchy-Euler Differential Equation [PDF]
Sahand Communications in Mathematical Analysis, 2021 In this paper, for a singular perturbation problem consist of the Cauchy-Euler equation with local and non-local boundary conditions. We investigate the condition of the self-adjoint and the non-self-adjoint, also look for the formation or non ...
Alireza Sarakhsi, Siamak Ashrafi
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Max-plus fundamental solution semigroups for a class of difference Riccati equations [PDF]
, 2015 Recently, a max-plus dual space fundamental solution semigroup for a class of difference Riccati equation (DRE) has been developed. This fundamental solution semigroup is represented in terms of the kernel of a specific max-plus linear operator that ...
Dower, Peter M., Zhang, Huan
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Mathematics in Engineering, 2020 We consider a Kolmogorov-Fokker-Planck operator of the kind: \[ \mathcal{L}u=\sum_{i,j=1}^{q}a_{ij}\left( t\right) \partial_{x_{i}x_{j}} ^{2}u+\sum_{k,j=1}^{N}b_{jk}x_{k}\partial_{x_{j}}u-\partial_{t}u,\qquad (x,t)\in\mathbb{R}^{N+1} \] where $\left\{ a_{
Marco Bramanti, Sergio Polidoro
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On the fundamental solution and a variational formulation of a degenerate diffusion of Kolmogorov type [PDF]
, 2017 In this paper, we construct the fundamental solution to a degenerate diffusion of Kolmogorov type and develop a time-discrete variational scheme for its adjoint equation.
M. H. Duong, H. M. Tran
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Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory [PDF]
, 2007 In this article we introduce the notion of fundamental solution in the Colombeau context as an element of the dual $\LL(\Gc(\R^n),\wt{\C})$. After having proved the existence of a fundamental solution for a large class of partial differential operators ...
Garetto, Claudia
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