Results 51 to 60 of about 1,356,954 (292)
Fundamental solutions for degenerate parabolic equations [PDF]
Acta Mathematica, 1974 This chapter explains the construction of a candidate for a fundamental solution and the existence, smoothness, and certain bounds for a fundamental solution Γ. The underlying assumptions were that ( a ij , ( x )) is uniformly positive definite and a ij , b i are bounded and uniformly Holder continuous. The chapter presents a proof of how if a ij ,
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Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ, 2010 The classification of the weak solutions to Dirichlet initial boundary value problemassociated with a linear degenerate parabolic equation has been studied. Some applications to associated optimal control problems in coeffcients are discussed.
I. G. Balanenko, P. I. Kogut
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Inhomogeneous parabolic equations on unbounded metric measure spaces [PDF]
, 2012 We study the inhomogeneous semilinear parabolic equation ut = Δu + up + f(x), with source term f independent of time and subject to f(x) ≥ 0 and with u(0, x) = φ(x) ≥ 0, for the very general setting of a metric measure space. By establishing Harnack-type
Hu, Jiaxin +5 more
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Advanced Engineering Materials, EarlyView.Postbuild annealing systematically modifies the phase fractions and morphology of EB‐PBF processed Mo–9Si–8B. Quantitative microstructure–property correlations reveal how controlled phase evolution enhances high‐temperature compressive strength and creep resistance.
Christopher Schmidt +5 more
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Coefficient inverse problem for the strongly degenerate parabolic equation
Karpatsʹkì Matematičnì Publìkacìï, 2023 The coefficient inverse problem for the degenerate parabolic equation is investigated. The minor coefficient of this equation is the polynomial of the first power with respect to the space variable with two unknown time-dependent functions.
N.M. Huzyk, P.Y. Pukach, M.I. Vovk
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Periodic solutions for a degenerate parabolic equation
Applied Mathematics Letters, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yuanyuan Ke, Rui Huang, Jiebao Sun
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Advanced Engineering Materials, EarlyView.This study examines Invar composites reinforced with titanium carbide (TiC) and titanium nitride (TiN) using laser powder bed fusion (LPBF). It presents the influence of reinforcements on microstructure, tensile properties, and thermal expansion. Results show that TiC effectively strengthens Invar while maintaining low thermal expansion, whereas TiN ...
Ayodeji Nathaniel Oyedeji +3 more
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An inverse backward problem for degenerate two-dimensional parabolic equation [PDF]
Opuscula Mathematica, 2020 This paper deals with the determination of an initial condition in the degenerate two-dimensional parabolic equation \[\partial_{t}u-\mathrm{div}\left(a(x,y)I_2\nabla u\right)=f,\quad (x,y)\in\Omega,\; t\in(0,T),\] where \(\Omega\) is an open, bounded ...
Khalid Atifi +2 more
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Density estimates on a parabolic spde [PDF]
, 2002 We consider a general class of parabolic spde's [formula] with (t, x) [member of] [0, T]×[0, 1] and [epsilon]Wt,x, [epsilon] > 0, a perturbed Gaussian space-time white noise.
Márquez-Carreras, D. +4 more
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Asymptotic expansions for degenerate parabolic equations
Comptes Rendus. Mathématique, 2014 We prove asymptotic convergence results for some analytical expansions of solutions to degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the uniformly parabolic case, with some a priori bounds on “short cylinders”, and we achieve short-time ...
PASCUCCI, ANDREA +2 more
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