Zobrazeno 1 - 10
of 511
pro vyhledávání: '"35l20"'
This work studies the inverse problem of photoacoustic tomography (more precisely, the acoustic subproblem) as the identification of a space-dependent source parameter. The model consists of a wave equation involving a time-fractional damping term to
Externí odkaz:
http://arxiv.org/abs/2411.06609
Autor:
Sobajima, Motohiro
In this paper, we mainly discuss asymptotic profiles of solutions to a class of abstract second-order evolution equations of the form $u''+Au+u'=0$ in real Hilbert spaces, where $A$ is a nonnegative selfadjoint operator. The main result is the asympt
Externí odkaz:
http://arxiv.org/abs/2410.19366
Autor:
Ghisi, Marina, Gobbino, Massimo
We consider a wave equation with a time-dependent propagation speed, whose potential oscillations are controlled through bounds on its first and second derivatives and by limiting the integral of the difference with a fixed constant. We investigate w
Externí odkaz:
http://arxiv.org/abs/2410.11483
Autor:
Özsarı, Türker, Susuzlu, İdem
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of these models
Externí odkaz:
http://arxiv.org/abs/2410.09994
The celebrated geometric control condition of Bardos, Lebeau, and Rauch is necessary and sufficient for wave observability [1,7] and exact controllability. It requires that any point in phase-space be transported by the generalized geodesic flow to t
Externí odkaz:
http://arxiv.org/abs/2407.02255
Autor:
Xu, Guixiang, Yang, Pengxuan
We consider the defocusing, cubic nonlinear wave equation with zero Dirichlet boundary value in the exterior $\Omega = \R^3\backslash \bar{ B}(0,1)$. We make use of the distorted Fourier transform in \cite{LiSZ:NLS, Taylor:PDE:II} to establish the di
Externí odkaz:
http://arxiv.org/abs/2406.05614
In this work we introduce the concept of generalized exponential $\mathfrak{D}$-pullback attractor for evolution processes, where $\mathfrak{D}$ is a universe of families in $X$, which is a compact and positively invariant family that pullback attrac
Externí odkaz:
http://arxiv.org/abs/2401.06631
Autor:
Wang, Christopher, Townsend, Alex
We construct the first rigorously justified probabilistic algorithm for recovering the solution operator of a hyperbolic partial differential equation (PDE) in two variables from input-output training pairs. The primary challenge of recovering the so
Externí odkaz:
http://arxiv.org/abs/2312.17489
Autor:
Ghisi, Marina, Gobbino, Massimo
We consider an abstract linear wave equation with a time-dependent dissipation that decays at infinity with the so-called scale invariant rate, which represents the critical case. We do not assume that the coefficient of the dissipation term is smoot
Externí odkaz:
http://arxiv.org/abs/2312.15531
In this paper, we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. The global behavior of the solutions with non-positive and sub-critical energy is completel
Externí odkaz:
http://arxiv.org/abs/2310.18775