scholarly journals Continuity of global attractors for a class of non local evolution equations

2010 ◽  
Vol 26 (3) ◽  
pp. 1073-1100 ◽  
Author(s):  
Antônio Luiz Pereira ◽  
◽  
Severino Horácio da Silva ◽  
Keyword(s):  
Evolution Equations ◽  
Global Attractors ◽  
Non Local

scholarly journals Asymptotic Smoothing and Global Attractors for a Class of Nonlinear Evolution Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Yongqin Xie ◽  
Zhufang He ◽  
Chen Xi ◽  
Zheng Jun
Keyword(s):  
Evolution Equations ◽  
Global Solutions ◽  
Global Attractors ◽  
Nonlinear Evolution Equations ◽  
Time Behavior ◽  
Asymptotic Regularity ◽  
Compact Attractor ◽  
Long Time ◽  
Critical Exponential Growth ◽  
Semilinear Evolution Equations

We prove the asymptotic regularity of global solutions for a class of semilinear evolution equations in H01(Ω)×H01(Ω). Moreover, we study the long-time behavior of the solutions. It is proved that, under the natural assumptions, these equations possess the compact attractor 𝒜 which is bounded in H2(Ω)×H2(Ω), where the nonlinear term f satisfies a critical exponential growth condition.

scholarly journals Using the Split Bregman Algorithm to Solve the Self-repelling Snakes Model

2022 ◽  
Author(s):  
Huizhu Pan ◽  
Jintao Song ◽  
Wanquan Liu ◽  
Ling Li ◽  
Guanglu Zhou ◽  
...  
Keyword(s):  
Evolution Equations ◽  
Active Contour Model ◽  
Operator Splitting ◽  
The Self ◽  
Convergence Time ◽  
Variational Model ◽  
Split Bregman ◽  
Geodesic Active Contour ◽  
Non Local ◽  
Split Bregman Algorithm

AbstractPreserving contour topology during image segmentation is useful in many practical scenarios. By keeping the contours isomorphic, it is possible to prevent over-segmentation and under-segmentation, as well as to adhere to given topologies. The Self-repelling Snakes model (SR) is a variational model that preserves contour topology by combining a non-local repulsion term with the geodesic active contour model. The SR is traditionally solved using the additive operator splitting (AOS) scheme. In our paper, we propose an alternative solution to the SR using the Split Bregman method. Our algorithm breaks the problem down into simpler sub-problems to use lower-order evolution equations and a simple projection scheme rather than re-initialization. The sub-problems can be solved via fast Fourier transform or an approximate soft thresholding formula which maintains stability, shortening the convergence time, and reduces the memory requirement. The Split Bregman and AOS algorithms are compared theoretically and experimentally.

Diffusion Effects Induced by Dislocations in Crystalline Materials Subjected to Large Strains

2015 ◽  
Vol 651-653 ◽  
pp. 89-95
Author(s):  
Raisa Paşcan ◽  
Sanda Cleja-Ţigoiu
Keyword(s):  
Evolution Equations ◽  
Plane Stress State ◽  
Large Strains ◽  
Slip Systems ◽  
State Variables ◽  
Equilibrium Equations ◽  
Crystalline Materials ◽  
Dislocation Densities ◽  
Differential Type ◽  
Non Local

Abstract. We reconsider here the FEM-algorithm for solving the initial and boundary value problems performed within the viscoplastic constitutive framework and proposed in our paper [1]. The problems concerning the deformation of a sheet composed of a single fcc-crystal, generated by different slip systems simultaneously activated, are solved numerically for an in-plane stress state. The variational formulation is associated to the incremental equilibrium equations and is coupled with an update procedure for the state variables, which are described by the differential type equations, as well as for the non-local evolution equations of the dislocation densities. The length scale parameter is introduced into the model through the diffusion-like parameter which enters the evolution equations for dislocation densities. For more accuracy of the simulation, the shape functions have been chosen polynomials with higher than one degree. We do not consider that once a slip system was activated it remains active for the rest of simulation. The activation condition is a key point in the numerical algorithm. As a numerical example, we perform a tensile test of a rectangular and non-rectangular metallic sheet, comparring the results of the simulation when two, respectively eight slip systems are considered.

scholarly journals Normal Hyperbolicity and Continuity of Global Attractors for a Nonlocal Evolution Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Severino Horácio da Silva ◽  
Jocirei Dias Ferreira ◽  
Flank David Morais Bezerra
Keyword(s):  
Evolution Equation ◽  
Lower Semicontinuity ◽  
Evolution Equations ◽  
Upper Semicontinuity ◽  
Global Attractors ◽  
Functional Parameter ◽  
Normal Hyperbolicity ◽  
Nonlocal Evolution Equations

We show the normal hyperbolicity property for the equilibria of the evolution equation∂m(r,t)/∂t=-m(r,t)+g(βJ*m(r,t)+βh),  h,β≥0,and using the normal hyperbolicity property we prove the continuity (upper semicontinuity and lower semicontinuity) of the global attractors of the flow generated by this equation, with respect to functional parameterJ.

scholarly journals Existence, uniqueness and stability results for semilinear integrodifferential non-local evolution equations with Random impulse

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6615-6626
Author(s):  
B. Radhakrishnan ◽  
M. Tamilarasi ◽  
P. Anukokila
Keyword(s):  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Semigroup Theory ◽  
Local Conditions ◽  
Fixed Point Approach ◽  
Non Local ◽  
The Stability ◽  
Random Impulse ◽  
Stability Results

In this paper, authors investigated the existence and uniqueness of random impulsive semilinear integrodifferential evolution equations with non-local conditions in Hilbert spaces. Also the stability results for the same evolution equation has been studied. The results are derived by using the semigroup theory and fixed point approach. An application is provided to illustrate the theory.

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