A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Nonlinear Science"
DOI: 10.1007/s00332-017-9414-1
Abstract: Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a… read more here.
Keywords: diffusion; speckle noise; diffusion equation; model ... See more keywords
Blow-Up Phenomena of a Cancer Invasion Model with Nonlinear Diffusion and Haptotaxis Term
Sign Up to like & getrecommendations! Published in 2020 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-020-00996-7
Abstract: In this paper, we consider a nonlinear cancer invasion mathematical model with proliferation, growth and haptotaxis effects. We obtain lower bounds for the finite-time blow-up of solutions of the considered system with nonlinear diffusion operator… read more here.
Keywords: blow; model; cancer invasion; nonlinear diffusion ... See more keywords
Submodels of model of nonlinear diffusion with non-stationary absorption
Sign Up to like & getrecommendations! Published in 2017 at "International Journal of Non-linear Mechanics"
DOI: 10.1016/j.ijnonlinmec.2017.02.011
Abstract: Abstract We study the model, describing a nonlinear diffusion process (or a heat propagation process) in an inhomogeneous medium with non-stationary absorption (or source). We found tree submodels of the original model of the nonlinear… read more here.
Keywords: diffusion process; diffusion; process; nonlinear diffusion ... See more keywords
Boundedness and global solvability to a chemotaxis model with nonlinear diffusion
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2017.06.034
Abstract: Abstract In this paper, we study a chemotaxis model with nonlinear diffusion Δ u m ( m > 1 ). We consider this problem in a bounded domain Ω ⊂ R 3 with zero-flux boundary… read more here.
Keywords: model nonlinear; boundedness global; chemotaxis model; nonlinear diffusion ... See more keywords
Global bounded weak solutions for a chemotaxis-Stokes system with nonlinear diffusion and rotation
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2021.04.020
Abstract: Abstract In this paper, we discuss the following chemotaxis-Stokes system with nonlinear diffusion and rotation { n t + u ⋅ ∇ n = Δ n m − ∇ ⋅ ( n S ( x… read more here.
Keywords: nonlinear diffusion; stokes system; chemotaxis stokes; system nonlinear ... See more keywords
The concavity of p-Rényi entropy power for doubly nonlinear diffusion equations and L-Gagliardo-Nirenberg-Sobolev inequalities
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.123698
Abstract: Abstract We prove the concavity of p-Renyi entropy power for positive solutions to the doubly nonlinear diffusion equations on R n or compact Riemannian manifolds with nonnegative Ricci curvature. As applications, we give new proofs… read more here.
Keywords: gagliardo nirenberg; diffusion equations; concavity; doubly nonlinear ... See more keywords
Nonlinear diffusion of gluons
Sign Up to like & getrecommendations! Published in 2022 at "Physica A: Statistical Mechanics and its Applications"
DOI: 10.1016/j.physa.2022.127299
Abstract: It is proposed to consider the fast thermalization of gluons in relativistic heavy-ion collisions as a diffusion process in momentum space. Closed-form analytical solutions of a nonlinear boson diffusion equation (NBDE) with constant drift and… read more here.
Keywords: diffusion gluons; diffusion; nonlinear diffusion;
Global existence to a chemotaxis-consumption model with nonlinear diffusion and singular sensitivity
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DOI: 10.1080/00036811.2018.1478083
Abstract: ABSTRACT This paper deals with the chemotaxis-consumption model with singular sensitivity and nonlinear diffusion under the homogenous Neumann boundary condition in a smooth-bounded domain , with positive parameters and , , for , m>1 and… read more here.
Keywords: consumption model; singular sensitivity; nonlinear diffusion; chemotaxis consumption ... See more keywords
Invasive-invaded system of non-Lipschitz porous medium equations with advection
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DOI: 10.1142/s1793524521500613
Abstract: This work provides analytical results towards applications in the field of invasive-invaded systems modeled with nonlinear diffusion and with advection. The results focus on showing regularity, existence and uniqueness of weak solutions using the condition… read more here.
Keywords: nonlinear diffusion; system non; invaded system; lipschitz porous ... See more keywords
Nonlinear diffusion in transparent media: The resolvent equation
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DOI: 10.1515/acv-2017-0002
Abstract: Abstract We consider the partial differential equation u - f = div ( u m ∇ u | ∇ u | ) u-f=\operatornamewithlimits{div}\biggl{(}u^{m}\frac{\nabla u}{|\nabla u|}% \biggr{)} with f nonnegative and bounded… read more here.
Keywords: diffusion transparent; resolvent equation; transparent media; nonlinear diffusion ... See more keywords
Gradient estimates for an orthotropic nonlinear diffusion equation
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DOI: 10.1515/acv-2021-0052
Abstract: Abstract We consider a quasilinear degenerate parabolic equation driven by the orthotropic p-Laplacian. We prove that local weak solutions are locally Lipschitz continuous in the spatial variable, uniformly in time. read more here.
Keywords: orthotropic nonlinear; estimates orthotropic; equation; diffusion equation ... See more keywords