Results 31 to 40 of about 73 (72)

Non-existence, radial symmetry, monotonicity, and Liouville theorem of master equations with fractional p-Laplacian

Advances in Nonlinear Analysis
In this article, first, we introduce a new operator (∂t−Δp)su(z,t)=Cn,sp∫−∞t∫Rn∣u(z,t)−u(ζ,ϱ)∣p−2(u(z,t)−u(ζ,ϱ))(t−ϱ)n2+1+sp2e−∣z−ζ∣24(t−ϱ)dζdϱ,{\left({\partial }_{t}-{\Delta }_{p})}^{s}u\left(z,t)={C}_{n,sp}\underset{-\infty }{\overset{t}{\int }}\mathop{
Liu Mengru, Zhang Lihong
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Sliding methods for dual fractional nonlinear divergence type parabolic equations and the Gibbons’ conjecture

Advanced Nonlinear Studies
In this paper, we consider the general dual fractional parabolic problem ∂tαu(x,t)+Lu(x,t)=f(t,u(x,t))inRn×R. ${\partial }_{t}^{\alpha }u\left(x,t\right)+\mathcal{L}u\left(x,t\right)=f\left(t,u\left(x,t\right)\right) \text{in} {\mathbb{R}}^{n}{\times ...
Guo Yahong, Ma Lingwei, Zhang Zhenqiu
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Well-posedness and maximum principles for lattice reaction-diffusion equations

Advances in Nonlinear Analysis, 2017
Existence, uniqueness and continuous dependence results together with maximum principles represent key tools in the analysis of lattice reaction-diffusion equations.
Slavík Antonín, Stehlík Petr, Volek Jonáš   +2 more
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On the well-posedness of a multiscale mathematical model for Lithium-ion batteries

Advances in Nonlinear Analysis, 2018
We consider the mathematical treatment of a system of nonlinear partial differential equations based on a model, proposed in 1972 by J. Newman, in which the coupling between the Lithium concentration, the phase potentials and temperature in the ...
Díaz J. Ildefonso, Gómez-Castro David, Ramos Angel M.   +2 more
doaj   +1 more source

Existence results for some anisotropic possible singular problems via the sub-supersolution method

Using the sub-super solution method, we prove the existence of the solutions for the following anisotropic problem with singularity, where Ω⊂RN is a bounded domain with smooth boundary and a given singular nonlinearity f : Ω×(0,∞)⟶[0,∞) f : Ω×(0,∞)⟶[0,∞).
FOUAD, Kissi, EL AMROUSS, Abdelrachid, ABDELLAH, Hamidi   +2 more
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Beyond the classical strong maximum principle: Sign-changing forcing term and flat solutions

Advances in Nonlinear Analysis
We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain can be extended, under suitable conditions, to the case in which the forcing term is sign ...
Díaz Jesús Ildefonso, Hernández Jesús   +1 more
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Moving planes and sliding methods for fractional elliptic and parabolic equations

Advanced Nonlinear Studies
In this paper, we summarize some of the recent developments in the area of fractional elliptic and parabolic equations with focus on how to apply the sliding method and the method of moving planes to obtain qualitative properties of solutions.
Chen Wenxiong, Hu Yeyao, Ma Lingwei
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Hopf's lemma, asymptotic radial symmetry, and monotonicity of solutions to the logarithmic Laplacian parabolic system

Advances in Nonlinear Analysis
In this article, we extend the asymptotic method of moving planes to the following logarithmic Laplacian parabolic system: ∂z∂t(η,t)+(−△)ℒz(η,t)=f(t,v(η,t)),(η,t)∈B1(0)×[0,∞),∂v∂t(η,t)+(−△)ℒv(η,t)=g(t,z(η,t)),(η,t)∈B1(0)×[0,∞),z(η,t)=0,v(η,t)=0,(η,t)∈B1c(
Wang Guotao, Wang Jing
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Asymptotic Stability of a Plane CJ Detonation Wave

, 2007
. We study the asymptotic stability of a plane CJ detonation wave under the assumption of small resolved heat release (SRHR). We prove that the solution exists globally and that the solution converges uniformly to a shifted CJ detonation wave as t!+ 1 ...
Tong Li
core  

Nonlinear Neumann Boundary Conditions for Quasilinear Degenerate Elliptic Equations and Applications

, 1999
We prove comparison results between viscosity sub and supersolutions of degenerate elliptic and parabolic equations associated to, possibly nonlinear, Neumann boundary conditions. These results are obtained under more general assumptions on the equation (
Guy Barles
core