Global bounded weak solutions and asymptotic behavior to a chemotaxis-Stokes model with non-Newtonian filtration slow diffusion

2021 ◽  
Vol 287 ◽  
pp. 148-184
Author(s):  
Chunhua Jin
Keyword(s):  
Asymptotic Behavior ◽  
Weak Solutions ◽  
Slow Diffusion ◽  
Bounded Weak Solutions

scholarly journals Local versus nonlocal elliptic equations: short-long range field interactions

2020 ◽  
Vol 10 (1) ◽  
pp. 895-921
Author(s):  
Daniele Cassani ◽  
Luca Vilasi ◽  
Youjun Wang
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Principle ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Spectral Properties ◽  
Fractional Laplacian ◽  
Coupling Parameter ◽  
Nonlocal Operators ◽  
The Maximum Principle ◽  
Regularity Results

Abstract In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian. We analyze spectral properties, establish the validity of the maximum principle, prove existence, nonexistence, symmetry and regularity results for weak solutions. The asymptotic behavior of weak solutions as the coupling parameter vanishes (which turns the problem into a purely nonlocal one) or goes to infinity (reducing the problem to the classical semilinear Laplace equation) is also investigated.

Local Hölder regularity for a doubly singular PDE

2018 ◽  
Vol 22 (03) ◽  
pp. 1850054
Author(s):  
Eurica Henriques
Keyword(s):  
Parabolic Equation ◽  
Weak Solutions ◽  
Iteration Method ◽  
Hölder Continuity ◽  
Hölder Regularity ◽  
Holder Continuity ◽  
Singular Parabolic Equation ◽  
Local Hölder Continuity ◽  
Singular Pde ◽  
Bounded Weak Solutions

We establish the local Hölder continuity for the nonnegative bounded weak solutions of a certain doubly singular parabolic equation. The proof involves the method of intrinsic scaling and the parabolic version of De Giorgi’s iteration method.

scholarly journals Asymptotic Behavior of Weak Solutions to the Generalized Nonlinear Partial Differential Equation Model

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Min Wu ◽  
Yousheng Wu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Asymptotic Behavior ◽  
Weak Solutions ◽  
Nonlinear Partial Differential Equation ◽  
Equation Model ◽  
Differential Equation Model ◽  
Partial Differential ◽  
Large Perturbation ◽  
Partial Differential Equation Model

This paper investigates the asymptotic behavior of weak solutions to the generalized nonlinear partial differential equation model. It is proved that every perturbed weak solution of the perturbed generalized nonlinear partial differential equations asymptotically converges to the solution of the original system under the large perturbation.

Bounded Weak Solutions for Hilfer Fractional Differential Equations on the Half Line

2020 ◽  
Vol 15 (1) ◽  
pp. 35
Author(s):  
Saıd Abbas ◽  
Ravi P. Agarwal ◽  
Mouffak Benchohra ◽  
Jamal Eddine Lazreg ◽  
Bashir Ahmad
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Half Line ◽  
Fractional Differential ◽  
Bounded Weak Solutions
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