Weak and strong solvability of parabolic variational inequalities in Banach spacesJournal of Evolution Equations - Tập 4 - Trang 497-517 - 2004
Matthew Rudd
We consider parabolic variational inequalities having the strong formulation
(1)
$$
\left\{ {\begin{array}{*{20}c}
{\left\langle {u'(t),\,v - \left. {u(t)} \right\rangle + \left\langle {Au(t),} \right.\,v - \left. {u(t)} \right\rangle + \Phi (v) - \Phi (u(t) \geq 0,} \right.} \\
{\forall v \in V^{**...... hiện toàn bộ
Diffusion-dominated asymptotics of solution to chemotaxis modelJournal of Evolution Equations - Tập 11 - Trang 509-529 - 2011
Andrzej Raczyński
The paper contains results on the asymptotic behavior, as t → +∞, of small solutions to simplified Keller–Segel problem modeling chemotaxis in the whole space
$${\mathbb R^2}$$
. We prove that the multiple of the heat kernel is a surprisingly good approximation of solutions.
The limitations of the Poincaré inequality for Grušin type operatorsJournal of Evolution Equations - Tập 14 - Trang 535-563 - 2014
Derek W. Robinson, Adam Sikora
We examine the validity of the Poincaré inequality for degenerate, second-order, elliptic operators H in divergence form on
$${L_2(\mathbf{R}^{n}\times \mathbf{R}^{m})}$$
. We assume the coefficients are real symmetric and
...... hiện toàn bộ
An inhomogeneous nonlocal diffusion problem with unbounded stepsJournal of Evolution Equations - Tập 16 - Trang 209-232 - 2015
Carmen Cortázar, Manuel Elgueta, Jorge García-Melián, Salomé Martínez
We consider the following nonlocal equation
$$\int J\left(\frac{x-y}{g(y)}
\right) \frac{u(y)}{g(y)} dy -u(x)=0\qquad x\in \mathbb{R},$$
where J is an even, compactly supported, Hölder continuous kernel with unit integral and g is a continuous pos...... hiện toàn bộ
Uniqueness for degenerate parabolic equations in weighted $$L^1$$ spacesJournal of Evolution Equations - Tập 22 - Trang 1-30 - 2022
Camilla Nobili, Fabio Punzo
We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, uniqueness is obtained for solutions that satisfy an appropriate integral condition; in particular, such condition holds for possibly unbounded solutions belonging to a suitable weighted
...... hiện toàn bộ