Results 31 to 40 of about 223 (46)
Advances in Nonlinear AnalysisWe consider the homogeneous Dirichlet problem for the parabolic equation ut−div(∣∇u∣p(x,t)−2∇u)=f(x,t)+F(x,t,u,∇u){u}_{t}-{\rm{div}}({| \nabla u| }^{p\left(x,t)-2}\nabla u)=f\left(x,t)+F\left(x,t,u,\nabla u) in the cylinder QT≔Ω×(0,T){Q}_{T}:= \Omega ...
Arora Rakesh, Shmarev Sergey
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Initial value problems for diffusion equations with singular potential [PDF]
, 2012 Let $V$ be a nonnegative locally bounded function defined in $Q_\infty:=\BBR^n\times(0,\infty)$. We study under what conditions on $V$ and on a Radon measure $\gm$ in $\mathbb{R}^d$ does it exist a function which satisfies $\partial_t u-\xD u+ Vu=0$ in ...
Gkikas, Konstantinos, Veron, Laurent
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Stability of non-isolated asymptotic profiles for fast diffusion
, 2015 The stability of asymptotic profiles of solutions to the Cauchy-Dirichlet problem for Fast Diffusion Equation (FDE, for short) is discussed. The main result of the present paper is the stability of any asymptotic profiles of least energy.
Akagi, Goro
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Quenching phenomenon of singular parabolic problems with L1 initial data [PDF]
, 2016 We extend some previous existence results for quenching type parabolic problems involving a negative power of the unknown in the equation to the case of merely integrable initial data.
Dao, A.N. +2 more
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When fast diffusion and reactive growth both induce accelerating invasions
, 2018 We focus on the spreading properties of solutions of monostable equations with fast diffusion. The nonlinear reaction term involves a weak Allee effect, which tends to slow down the propagation.
Alfaro, Matthieu, Giletti, Thomas
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A critical non-homogeneous heat equation with weighted source
European Journal of Applied MathematicsSome qualitative properties of radially symmetric solutions to the non-homogeneous heat equation with critical density and weighted source \begin{align*} |x|^{-2}\partial _tu=\Delta u+|x|^{\sigma }u^p, \quad (x,t)\in {\mathbb {R}}^N\times (0,T), \end ...
Razvan Gabriel Iagar, Ariel Sánchez
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On a singular heat equation with dynamic boundary conditions
, 2015 In this paper we analyze a nonlinear parabolic equation characterized by a singular diffusion term describing very fast diffusion effects. The equation is settled in a smooth bounded three-dimensional domain and complemented with a general boundary ...
Alikakos +16 more
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The stochastic porous media equation in $\R^d$
, 2014 Existence and uniqueness of solutions to the stochastic porous media equation $dX-\D\psi(X) dt=XdW$ in $\rr^d$ are studied. Here, $W$ is a Wiener process, $\psi$ is a maximal monotone graph in $\rr\times\rr$ such that $\psi(r)\le C|r|^m$, $\ff r\in\rr$, $
Barbu, Viorel +2 more
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Integrability of the derivative of solutions to a singular one-dimensional parabolic problem
, 2017 We study integrability of the derivative of solutions to a singular one-dimensional parabolic equation with initial data in $W^{1,1}$. In order to avoid additional difficulties we consider only the periodic boundary conditions.
Nakayasu, Atsushi, Rybka, Piotr
core
Molecular Resources from Transcriptomes in the Brassicaceae Family. [PDF]
Front Plant Sci, 2017 Lopez L +4 more
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