Grain boundary grooving in a bicrystal with passivation coating
Sign Up to like & getrecommendations! Published in 2021 at "Continuum Mechanics and Thermodynamics"
DOI: 10.1007/s00161-021-01040-0
Abstract: We use the sixth-order linear parabolic equation $$\begin{aligned} \frac{\partial y}{\partial t}=B\left( \alpha \frac{\partial ^{6}y}{\partial x^{6}}-\frac{\partial ^{4}y}{\partial x^{4}}\right) ,\ x\in {\mathbb {R}}_{+},\ t>0, \end{aligned}$$ proposed by Rabkin and describing the evolution of a solid surface covered… read more here.
Keywords: grain boundary; passivation; frac partial; boundary grooving ... See more keywords
On a Class of Critical p-Biharmonic Kirchhoff Type Problems with Indefinite Weights
Sign Up to like & getrecommendations! Published in 2020 at "Bulletin of The Iranian Mathematical Society"
DOI: 10.1007/s41980-020-00436-z
Abstract: Using the genus theory introduced by Krasnoselskii and a variant of the mountain pass theorem due to Rabinowitz [24], we study the existence of solutions for the following Kirchhoff type problem: $$\begin{aligned} {\left\{ \begin{array}{ll} M\left(… read more here.
Keywords: class critical; kirchhoff; delta; partial partial ... See more keywords
On effective field theory of F-theory beyond leading order
Sign Up to like & getrecommendations! Published in 2019 at "Classical and Quantum Gravity"
DOI: 10.1088/1361-6382/aaf86e
Abstract: We construct a proposal for effective bosonic field theory at order $ \alpha'^3 $ in twelve dimensions, whose compactification on a circle and on a torus respectively yields eleven-dimensional and type IIB supergravity theories at… read more here.
Keywords: type iib; order; theory; field ... See more keywords
On the Surface Integral Approximation of the Second Derivatives of the Potential of a Bulk Charge Located in a Layer of Small Thickness
Sign Up to like & getrecommendations! Published in 2018 at "Differential Equations"
DOI: 10.1134/s0012266118090112
Abstract: We consider a bulk charge potential of the form $$u(x) = \int\limits_\Omega {g(y)F(x - y)dy,x = ({x_1},{x_2},{x_3}) \in {\mathbb{R}^3},} $$u(x)=∫Ωg(y)F(x−y)dy,x=(x1,x2,x3)∈R3, where Ω is a layer of small thickness h > 0 located around the midsurface… read more here.
Keywords: surface; second derivatives; partial partial; bulk charge ... See more keywords
Some properties of the solution to fractional heat equation with a fractional Brownian noise
Sign Up to like & getrecommendations! Published in 2017 at "Advances in Difference Equations"
DOI: 10.1186/s13662-017-1151-0
Abstract: In this paper, we consider the stochastic heat equation of the form ∂u∂t=Δαu+∂2B∂t∂x,$$\frac{\partial u}{\partial t}=\Delta_{\alpha}u+\frac{\partial ^{2}B}{\partial t\,\partial x}, $$ where ∂2B∂t∂x$\frac{\partial^{2}B}{\partial t\,\partial x}$ is a fractional Brownian sheet with Hurst indices H1,H2∈(12,1)$H_{1},H_{2}\in(\frac{1}{2},1)$ and Δα=−(−Δ)α/2$\Delta _{\alpha}=-(-\Delta)^{\alpha/2}$… read more here.
Keywords: alpha; fractional brownian; partial partial; heat equation ... See more keywords