Results 21 to 30 of about 233,661 (218)
Partial Differential Equations in Applied Mathematics, 2023 In this paper, we focus on solving semilinear parabolic differential equations in low and high-dimensional spaces by using backward stochastic differential equations and deep neural networks (the BSDE solver introduced by Han et al. in 2017).
Shawn Koohy +2 more
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On Oscillations in a Gene Network with Diffusion
Mathematics, 2023 We consider one system of partial derivative equations of the parabolic type as a model of a simple 3D gene network in the presence of diffusion of its three components.
Vladimir Golubyatnikov +2 more
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Case Studies in Thermal Engineering, 2023 Current investigation deals with the melting heat transfer for the Jeffrey hybrid-nanofluid flow in parabolic trough solar collectors through Darcy Forchheimer porous media over a variable thick vertical elongation Riga surface under the effect of solar ...
Bhupendra K. Sharma +4 more
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Higher-order parabolic equations with VMO assumptions and general boundary conditions with variable leading coefficients [PDF]
, 2017 We prove weighted mixed $L_{p}(L_{q})$-estimates, with $p,q\in(1,\infty)$, for higher-order elliptic and parabolic equations on the half space $\mathbb{R}^{d+1}_{+}$ and on domains with general boundary conditions which satisfy the Lopatinskii--Shapiro ...
Hongjie Dong, C. Gallarati
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Case Studies in Thermal Engineering, 2023 This attempt numerically investigates the heat transfer in parabolic trough solar collectors due to the rotating tube for the hybrid nanofluid flow over the Riga surface with Darcy Forchheimer’s porous medium under the effect of solar radiation.
B.K. Sharma +3 more
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Higher order parabolic boundary Harnack inequality in C1 and Ck, α domains
Discrete and Continuous Dynamical Systems. Series A, 2022 We study the boundary behaviour of solutions to second order parabolic linear equations in moving domains. Our main result is a higher order boundary Harnack inequality in C1 and Ck, α domains, providing that the quotient of two solutions vanishing on ...
Teo Kukuljan
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On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach [PDF]
, 2009 The classic problem of regularity of boundary points for higher-order partial differential equations (PDEs) is concerned. For second-order elliptic and parabolic equations, this study was completed by Wiener’s (J. Math. Phys. Mass. Inst. Tech. 3:127–146,
V. Galaktionov
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Universal estimate of the gradient for parabolic equations [PDF]
, 2008 We suggest a modification of the estimate for weighted Sobolev norms of solutions of parabolic equations such that the matrix of the higher order coefficients is included into the weight for the gradient. More precisely, we found the upper limit estimate
Dokuchaev N G +4 more
core +6 more sources
Higher order nonlinear degenerate parabolic equations
Journal of Differential Equations, 1990 The paper deals with a few existence and positivity results for higher order, possibly degenerate, nonlinear parabolic equations. The equations under investigation are of the type \[ \frac{du}{dt}+\frac{\partial}{\partial \kappa}(f(u)\frac{\partial^{2m+1}u}{\partial \kappa^{2m+1}})=0 \] where \(f(u)=| u|^ m\) \(f_ 0(u)\) with \(n\geq 1\) and \(f_ 0(u ...
Bernis, Francisco, Friedman, Avner
openaire +2 more sources
Higher order Schauder estimates for degenerate or singular parabolic equations [PDF]
Revista matemática iberoamericanaIn this paper, we complete the analysis initiated in [Calc. Var. Partial Differential Equations 63 (2024), article no. 204] establishing some higher order C^{k+2,\alpha} Schauder estimates ( k \in \mathbb{N} ) for a class of parabolic ...
A. Audrito +2 more
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