نتایج جستجو برای: nonlocal strain gradient

تعداد نتایج: 354122  

2008
DONG LI XIAOYI ZHANG

We consider a nonlocal aggregation equation with nonlinear diffusion which arises from the study of biological aggregation dynamics. As a degenerate parabolic problem, we prove the well-posedness, continuation criteria and smoothness of local solutions. For compactly supported nonnegative smooth initial data we prove that the gradient of the solution develops L∞ x -norm blowup in finite time.

Journal: :SIAM J. Control and Optimization 2011
Pierre Cardaliaguet Catherine Rainer

Viscosity solutions of fully nonlinear, local or non local, Hamilton-Jacobi equations with a super-quadratic growth in the gradient variable are proved to be Hölder continuous, with a modulus depending only on the growth of the Hamiltonian. The proof involves some representation formula for nonlocal Hamilton-Jacobi equations in terms of controlled jump processes and a weak reverse inequality.

2012
Qiang Du Kun Zhou

Well-posedness results for the state-based peridynamic nonlocal continuum model of solid mechanics are established with the help of a nonlocal vector calculus. The peridynamic strain energy density for an elastic constitutively linear anisotropic heterogenous solid is expressed in terms of the field operators of that calculus, after which a variational principle for the equilibrium state is def...

2007
Jesenko Vukadinovic

The existence of inertial manifolds for a Smoluchowski equation – a nonlinear Fokker-Planck equation on the unit sphere which arises in modeling of colloidal suspensions – is investigated. A nonlinear and nonlocal transformation is used to eliminate the gradient from the nonlinear term.

Journal: :Physical review letters 2004
I V Grigorieva A K Geim S V Dubonos K S Novoselov D Y Vodolazov F M Peeters P H Kes M Hesselberth

We report a new nonlocal effect in vortex matter, where an electric current confined to a small region of a long and sufficiently narrow superconducting wire causes vortex flow at distances hundreds of intervortex separations away. The observed remote traffic of vortices is attributed to a very efficient transfer of a local strain through the one-dimensional vortex lattice (VL), even in the pre...

Journal: :International Journal of Solids and Structures 2006

Journal: :Journal of Differential Equations 2021

We prove existence of solutions and study the nonlocal-to-local asymptotics for nonlocal, convective, Cahn-Hilliard equations in case a W^{1,1} convolution kernel under homogeneous Neumann conditions. Any type potential, possibly also double-obstacle or logarithmic type, is included. Additionally, we highlight variants extensions to setting periodic boundary conditions viscosity contributions, ...

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