Journal of Evolution Equations
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Boundedness and asymptotic behavior in a fully parabolic chemotaxis-growth system with signal-dependent sensitivity
Journal of Evolution Equations - Tập 17 - Trang 909-929 - 2016
This paper deals with a fully parabolic chemotaxis-growth system with signal-dependent sensitivity
$$\left\{\begin{array}{ll}u_t=\Delta u-\nabla\cdot(u\chi(v)\nabla v)+\mu u(1-u), \quad &\quad(x,t)\in\Omega\times (0,\infty),\\ v_{t}=\varepsilon \Delta v+h(u,v), \quad &\quad(x,t)\in \Omega\times (0,\infty),\end{array}\rig...... hiện toàn bộ
Regularity and time behavior of the solutions to weak monotone parabolic equations
Journal of Evolution Equations - - 2021
In this paper, we study the behavior in time of the solutions for a class of parabolic problems including the p-Laplacian equation and the heat equation. Either the case of singular or degenerate equations is considered. The initial datum
$$u_0$$
is a summable function and a reaction term f is pre...... hiện toàn bộ
The Gevrey analyticity and decay for the micropolar system in the critical Besov space
Journal of Evolution Equations - Tập 21 - Trang 4751-4771 - 2021
In this paper, we are concerned with the 3-D incompressible micropolar fluid system, which is a non-Newtonian fluid exhibiting micro-rotational effects and micro-rotational inertia. We aim at establishing the global Gevrey analyticity in the critical Besov space. As a first step, inspired by Chemin’s work (J Anal Math 77:27–50, 1999), we construct the global-in-time existence of the strong solutio...... hiện toàn bộ
Entropy solutions to a non-conservative and non-strictly hyperbolic diagonal system inspired by dislocation dynamics
Journal of Evolution Equations - Tập 23 - Trang 1-35 - 2023
In this work, we study the existence of solutions to a
$$2\times 2$$
non-conservative and non-strictly hyperbolic system in one space dimension related to the dynamics of dislocation densities in crystallography, propagating in two opposite directions. For such systems, existence results are mainl...... hiện toàn bộ
Optimal regularity and exponential stability for the Blackstock–Crighton equation in L p -spaces with Dirichlet and Neumann boundary conditions
Journal of Evolution Equations - Tập 16 - Trang 945-981 - 2016
The Blackstock–Crighton equation models nonlinear acoustic wave propagation in monatomic gases. In the present work, we investigate the associated inhomogeneous Dirichlet and Neumann boundary value problems in a bounded domain and prove long-time well-posedness and exponential stability for sufficiently small data. The solution depends analytically on the data. In the Dirichlet case, the solution ...... hiện toàn bộ
Anti-periodic solutions for nonlinear evolution inclusions
Journal of Evolution Equations - Tập 18 - Trang 1025-1047 - 2018
We consider an anti-periodic evolution inclusion defined on an evolution triple of spaces, driven by an operator of monotone-type and with a multivalued reaction term F(t, x). We prove existence theorem for the “convex” problem (that is, F is convex-valued) and for the “nonconvex” problem (that is, F is nonconvex-valued) and we also show the existence of extremal trajectories (that is, when F is r...... hiện toàn bộ
On the critical exponent and sharp lifespan estimates for semilinear damped wave equations with data from Sobolev spaces of negative order
Journal of Evolution Equations - Tập 23 - Trang 1-21 - 2023
We study semilinear damped wave equations with power nonlinearity
$$|u|^p$$
and initial data belonging to Sobolev spaces of negative order
$$\dot{H}^{-\gamma }$$
. In the present paper, we obtain a...... hiện toàn bộ
Small time asymptotics of diffusion processes
Journal of Evolution Equations - Tập 7 Số 1 - Trang 79-112 - 2007
Stable and unstable manifolds for quasilinear parabolic systems with fully nonlinear boundary conditions
Journal of Evolution Equations - Tập 6 - Trang 537-576 - 2006
We investigate quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions on bounded or exterior domains in the setting of Sobolev–Slobodetskii spaces. We establish local wellposedness and study the time and space regularity of the solutions. Our main results concern the asymptotic behavior of the solutions in the vicinity of a hyperbolic equilibrium. ...... hiện toàn bộ
Stability estimates for semigroups in the Banach case
Journal of Evolution Equations - - 2024
The purpose of this paper is to revisit previous works of the author with Helffer and Sjöstrand (
arXiv:1001.4171v1
. 2010; Int Equ Op Theory 93(3):36, 2021) on the stability of semigroups which were proved in the Hilbert case by considering the Banach case at the light of a paper by Latushkin and Yurov (Discrete Contin Dyn Syst 33:5203–5216, 2013).
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