Results 31 to 40 of about 248 (61)

Optimal global second-order regularity and improved integrability for parabolic equations with variable growth

Advances in Nonlinear Analysis
We 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
doaj   +1 more source

Blow up profiles for a quasilinear reaction-diffusion equation with weighted reaction

, 2019
We perform a thorough study of the blow up profiles associated to the following second order reaction-diffusion equation with non-homogeneous reaction: $$ \partial_tu=\partial_{xx}(u^m) + |x|^{\sigma}u^p, $$ in the range of exponents $10$.
Iagar, Razvan Gabriel, Sánchez, Ariel
core   +1 more source

The Yamabe flow on incomplete manifolds

, 2017
This article is concerned with developing an analytic theory for second order nonlinear parabolic equations on singular manifolds. Existence and uniqueness of solutions in an Lp-framework is established by maximal regularity tools.
Shao, Yuanzhen
core   +1 more source

A critical non-homogeneous heat equation with weighted source

European Journal of Applied Mathematics
Some 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
doaj   +1 more source

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
core   +2 more sources

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, Russo, Francesco, Röckner, Michael   +2 more
core  

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, Wolf EM, Pires JC, Edger PP, Koch MA.   +4 more
europepmc   +1 more source

Quantitative unique continuation for the heat equations with inverse square potential. [PDF]

J Inequal Appl, 2018
Zheng G, Li K, Zhang Y.
europepmc   +1 more source

Variational approach to coarse-graining of generalized gradient flows. [PDF]

Calc Var Partial Differ Equ, 2017
Duong MH, Lamacz A, Peletier MA, Sharma U.   +3 more
europepmc   +1 more source