Results 11 to 20 of about 116 (91)
Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type
Open Mathematics, 2023 The Cauchy problem in Rn{{\mathbb{R}}}^{n}, n≥2n\ge 2, for ut=Δu−∇⋅(uS⋅∇v),0=Δv+u,(⋆)\begin{array}{r}\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}{u}_{t}=\Delta u-\nabla \cdot \left(uS\cdot \nabla v),\\ 0=\Delta v+u,\end{array}\right.\hspace{2 ...
Winkler Michael
doaj +1 more source
The evolution of immersed locally convex plane curves driven by anisotropic curvature flow
Advances in Nonlinear Analysis, 2022 In this article, we study the evolution of immersed locally convex plane curves driven by anisotropic flow with inner normal velocity V=1αψ(x)καV=\frac{1}{\alpha }\psi \left(x){\kappa }^{\alpha } for α1\alpha \gt 1, where x∈[0,2mπ]x\in \left[0,2m\pi ] is
Wang Yaping, Wang Xiaoliu
doaj +1 more source
Open Mathematics, 2022 In this paper, we study the existence of solutions for the neutral evolution equations with nonlocal conditions and delay in α\alpha -norm, which are more general than in many previous publications.
Zhang Xuping, Sun Pan
doaj +1 more source
Advances in Nonlinear Analysis, 2023 We consider the nonlinear elliptic–parabolic boundary value problem involving the Dirichlet-to-Neumann operator of p-Laplace type at the critical Sobolev exponent.
Deng Yanhua, Tan Zhong, Xie Minghong
doaj +1 more source
Anisotropic 𝑝-Laplacian Evolution of Fast Diffusion Type
Advanced Nonlinear Studies, 2021 We study an anisotropic, possibly non-homogeneous version of the evolution 𝑝-Laplacian equation when fast diffusion holds in all directions. We develop the basic theory and prove symmetrization results from which we derive sharp L1L^{1}-L∞L^{\infty ...
Feo Filomena +2 more
doaj +1 more source
Double-phase parabolic equations with variable growth and nonlinear sources
Advances in Nonlinear Analysis, 2022 We study the homogeneous Dirichlet problem for the parabolic equations ut−div(A(z,∣∇u∣)∇u)=F(z,u,∇u),z=(x,t)∈Ω×(0,T),{u}_{t}-{\rm{div}}\left({\mathcal{A}}\left(z,| \nabla u| )\nabla u)=F\left(z,u,\nabla u),\hspace{1.0em}z=\left(x,t)\in \Omega \times ...
Arora Rakesh, Shmarev Sergey
doaj +1 more source
Anomalous pseudo-parabolic Kirchhoff-type dynamical model
Advances in Nonlinear Analysis, 2021 In this paper, we study an anomalous pseudo-parabolic Kirchhoff-type dynamical model aiming to reveal the control problem of the initial data on the dynamical behavior of the solution in dynamic control system. Firstly, the local existence of solution is
Dai Xiaoqiang +3 more
doaj +1 more source
Advanced Nonlinear Studies, 2020 We consider the high-dimensional equation ∂tu-Δum+u-βχ{u>0}=0{\partial_{t}u-\Delta u^{m}+u^{-\beta}{\chi_{\{u>0\}}}=0}, extending the mathematical treatment made in 1992 by B. Kawohl and R. Kersner for the one-dimensional case.
Dao Nguyen Anh +2 more
doaj +1 more source
Moroccan Journal of Pure and Applied Analysis, 2017 In this paper, we prove the existence of in finitely many solutions for the following system by applying a critical point variational principle obtained by Ricceri as a consequence of a more general variational principle and the theory of the ...
Ahmed A. +2 more
doaj +1 more source
On the relativistic heat equation in one space dimension
Proceedings of the London Mathematical Society, Volume 107, Issue 6, Page 1395-1423, December 2013., 2013 We study the relativistic heat equation in one space dimension. We prove a local regularity result when the initial datum is locally Lipschitz in its support. We propose a numerical scheme that captures the known features of the solutions and allows for analysing further properties of their qualitative behaviour.
J. A. Carrillo, V. Caselles, S. Moll
wiley +1 more source