Journal of Evolution Equations
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The Cayley transform of the generator of a polynomially stable $$C_0$$-semigroup
Journal of Evolution Equations - Tập 21 Số 4 - Trang 4575-4597 - 2021
AbstractIn this paper, we study the decay rate of the Cayley transform of the
generator of a polynomially stable $$C_0$$ C 0 -semigroup. To estimate the decay
rate of the Cayley transform, we develop an integral condition on resolvents for
polynomial stability. Using this integral condition, we relate polynomial
stability to Lyapunov equations. We also study robustness of polynomial
stability for ...
Weak and strong solvability of parabolic variational inequalities in Banach spaces
Journal of Evolution Equations - Tập 4 - Trang 497-517 - 2004
We consider parabolic variational inequalities having the strong formulation (1)
$$ \left\{ {\begin{array}{*{20}c} {\left\langle {u'(t),\,v - \left. {u(t)}
\right\rangle + \left\langle {Au(t),} \right.\,v - \left. {u(t)} \right\rangle +
\Phi (v) - \Phi (u(t) \geq 0,} \right.} \\ {\forall v \in V^{**} ,\,a.e.\,t \geq
0,} \\ \end{array} } \right. $$ where % MathType!Translator!2!1!AMS
LaTeX.tdl!TeX ...
Diffusion-dominated asymptotics of solution to chemotaxis model
Journal of Evolution Equations - Tập 11 - Trang 509-529 - 2011
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.
Mathematical analysis of a scalar multidimensional conservation law with discontinuous flux
Journal of Evolution Equations - - 2011
The limitations of the Poincaré inequality for Grušin type operators
Journal of Evolution Equations - Tập 14 - Trang 535-563 - 2014
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
$${a_1H_\delta\geq H\geq a_2H_\delta}$$ for some $${a_1,a_2>0}$$ where H δ is a
generalized Grušin operator,
$$H_\delta=-\nabla_{x_1}\,|x_1|^{\left(2\delta_1,2\delta_1'\right)}
...
Analyticity of solutions to fully nonlinear parabolic evolution equations on symmetric spaces
Journal of Evolution Equations - Tập 3 Số 4 - Trang 549-576 - 2003
Homogeneous Sobolev global-in-time maximal regularity and related trace estimates
Journal of Evolution Equations - Tập 24 - Trang 1-30 - 2024
In this paper, we prove global-in-time $$\dot{\textrm{H}}^{\alpha ,q}$$ -maximal
regularity for a class of injective, but not invertible, sectorial operators on
a UMD Banach space X, provided $$q\in (1,+\infty )$$ , $$\alpha \in
(-1+1/q,1/q)$$ . We also prove the corresponding trace estimate, so that the
solution to the canonical abstract Cauchy problem is continuous with values in a
not necessari...
Higher-dimensional moving singularities in a superlinear parabolic equation
Journal of Evolution Equations - Tập 18 Số 4 - Trang 1575-1593 - 2018
An inhomogeneous nonlocal diffusion problem with unbounded steps
Journal of Evolution Equations - Tập 16 - Trang 209-232 - 2015
We consider the following nonlocal equation $$\int J\left(\frac{x-y}{g(y)}
\right) \frac{u(y)}{g(y)} dy -u(x)=0\qquad x\in \mathbb{R},$$ where J is an
even, compactly supported, Hölder continuous kernel with unit integral and g is
a continuous positive function. Our main concern will be with unbounded
functions g, contrary to previous works. More precisely, we study the influence
of the growth of ...
Uniqueness for degenerate parabolic equations in weighted $$L^1$$ spaces
Journal of Evolution Equations - Tập 22 - Trang 1-30 - 2022
We study uniqueness of solutions to degenerate parabolic problems, posed in
bounded domains, where no boundary conditions are imposed. Under suitable
assumptions on the operator, uniqueness is obtained for solutions that satisfy
an appropriate integral condition; in particular, such condition holds for
possibly unbounded solutions belonging to a suitable weighted $$L^1$$ space....
Tổng số: 787
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