Classical solution to a 1-periodic initial value problem of parabolic type coupled with operators

Huan, Zhang; Huang, Haiyang; Kong, Linghai; Guo, Boling

doi:10.1016/j.cnsns.2005.05.005

Cited by 2 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where C i are constants depending only on u 0 ∞ , L, σ , λ, K, the reader might check [15] for details. A standard argument by maximum principle shows that To obtain a bound for Du α for u ∈ , we need a corollary to a theorem in [22].…”

Section: Appendixmentioning

confidence: 99%

See 1 more Smart Citation

A feature-oriented forward–backward diffusion model for intensity image restoration based on level set motion

Huan

Kong

Zuo

2009

International Journal of Computer Mathematics

Self Cite

View full text Add to dashboard Cite

In this paper, a new enhancing and smoothing partial differential equation coupled with time-delay regularization is presented, which is based on local geometric properties desired for image restoration. To reverse the process of image deterioration, a newly defined shock filter for edge enhancing is combined with a level set motion-based regularization equation. The balance between the backward process and the forward process is carried out by a weighting function coupled with time-delay regularization helping to identify boundary areas and homogeneous regions in a given image. The proposed model is well-posed in terms of viscosity solutions -the existence and uniqueness of periodic viscosity solution to the initial value problem of the equation is established. Numerical results for some kinds of grey-level images are demonstrated to confirm our anticipation.

show abstract

Section: Appendixmentioning

confidence: 99%

“…We follow the procedures given in [15]. The regularization problem (RI) corresponding to the initial value problem (CI) is formulated as follows.…”

Section: Appendixmentioning

confidence: 99%