Zobrazeno 1 - 10
of 436
pro vyhledávání: '"35g25"'
We consider the system of viscoelasticity with higher-order gradients and nonconvex energy in several space dimensions. We establish the asymptotic limits when the viscosity $\nu\rightarrow 0$ or when the dispersion coefficient $\delta \rightarrow 0$
Externí odkaz:
http://arxiv.org/abs/2410.17115
In this paper, we study the Cauchy problem for the linear plate equation with mass term and its applications to semilinear models. For the linear problem we obtain $L^p-L^q$ estimates for the solutions in the full range $1\leq p\leq q\leq \infty$, an
Externí odkaz:
http://arxiv.org/abs/2406.17211
In this paper, we study the Cauchy problem to the linear damped $\sigma$-evolution equation with time-dependent damping in the effective cases \begin{equation*} u_{t t}+(-\Delta)^\sigma u+b(t)(-\Delta)^\delta u_t=0, \end{equation*} and investigate th
Externí odkaz:
http://arxiv.org/abs/2404.06855
Autor:
Guo, Yingying, Ye, Weikui
In this paper, we consider the Cauchy problem for the $b$-equation. Firstly, for $s>\frac32,$ if $u_{0}(x)\in H^{s}(\mathbb{R})$ and $m_{0}(x)=u_{0}(x)-u_{0xx}(x)\in L^{1}(\mathbb{R}),$ the global solutions of the $b$-equation is established when $b\
Externí odkaz:
http://arxiv.org/abs/2402.15128
This paper reviews the results of existence and uniqueness of the solutions of these equations: the Korteweg-de Vries equation, the Kuramoto-Sivashinsky equation, the generalized Korteweg-de Vries-Kuramoto-Sivashinski equation and the non homogeneous
Externí odkaz:
http://arxiv.org/abs/2402.07172
Publikováno v:
ESAIM: Control, Optimisation and Calculus of Variations, 20(04), pp 1181-1202 (2014)
This paper deals with the distributed and boundary controllability of the so called Leray-$\alpha$ model. This is a regularized variant of the Navier-Stokes system ($\alpha$ is a small positive parameter) that can also be viewed as a model for turbul
Externí odkaz:
http://arxiv.org/abs/2402.06307
Publikováno v:
Advances in Differential Equations, 18(9/10), pp 935 - 954 (2013)
This work is devoted to prove the local null controllability of the Burgers-$\alpha$ model. The state is the solution to a regularized Burgers equation, where the transport term is of the form $zy_x$, $z=(Id-\alpha^2\frac{\partial^2}{\partial x^2})^{
Externí odkaz:
http://arxiv.org/abs/2402.06301
Autor:
Garénaux, Louis, de Rijk, Björn
For a viscous Klein-Gordon equation with quadratic nonlinearity, we prove that small solutions exist on exponentially long time scale. Our approach is based on the space-time resonance method in a diffusive setting. It allow to identify, through a si
Externí odkaz:
http://arxiv.org/abs/2402.02220
Autor:
Prykarpatskyy, Yarema
The paper investigates the Poisson structures associated with dynamical systems of the heavenly type, focusing on the Mikhalev-Pavlov and Pleba\'nski equation. The dynamical system is represented as a Hamiltonian system on a functional manifold, and
Externí odkaz:
http://arxiv.org/abs/2312.05618
In this article we investigate the asymptotic profile of solutions for the Cauchy problem of the nonlinear damped beam equation with two variable coefficients: \[ \partial_t^2 u + b(t) \partial_t u - a(t) \partial_x^2 u + \partial_x^4 u = \partial_x
Externí odkaz:
http://arxiv.org/abs/2310.18878