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pro vyhledávání: '"35L71"'
In this paper, blowup phenomenon for the semilinear wave equation with time-dependent speed of propagation and scattering damping is considered under the smallness of initial data. Our result contains small data blowup for sub-Strauss exponent for th
Externí odkaz:
http://arxiv.org/abs/2412.08834
Autor:
Shao, Kerun
We study the existence of global solutions to semilinear wave equations on exterior domains $\mathbb{R}^n\setminus\mathcal{K}$, $n\geq2$, with small initial data and nonlinear terms $F(\partial u)$ where $F\in C^\kappa$ and $\partial^{\leq\kappa}F(0)
Externí odkaz:
http://arxiv.org/abs/2412.05544
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:
Barashkov, Nikolay, Laarne, Petri
We study the expected transition frequency between the two metastable states of a stochastic wave equation with double-well potential. By transition state theory, the frequency factorizes into two components: one depends only on the invariant measure
Externí odkaz:
http://arxiv.org/abs/2410.03495
Autor:
Boughrara, Maissâ, Zaag, Hatem
We consider the semilinear wave equation with a power nonlinearity in the radial case. Given $r_0>0$, we construct a blow-up solution such that the solution near $(r_0,T(r_0))$ converges exponentially to a soliton. Moreover, we show that $r_0$ is a n
Externí odkaz:
http://arxiv.org/abs/2410.00636
We study the large deviation principle (LDP) for locally damped nonlinear wave equations perturbed by a bounded noise. When the noise is sufficiently non-degenerate, we establish the LDP for empirical distributions with lower bound of a local type. T
Externí odkaz:
http://arxiv.org/abs/2409.11717
Autor:
Sasaki, Takiko, Takamura, Hiroyuki
This note is a supplement with a new result to the review paper by Takamura [13] on nonlinear wave equations in one space dimension. We are focusing here to the long-time existence of classical solutions of semilinear wave equations in one space dime
Externí odkaz:
http://arxiv.org/abs/2409.06378
Autor:
D'Abbicco, Marcello
In this note, we prove the global existence of solutions to the semilinear damped wave equation in $\mathbb{R}^n$, $n\leq6$, with critical nonlinearity under the assumption that the initial data are small in the energy space $H^1\times L^2$ and under
Externí odkaz:
http://arxiv.org/abs/2408.11756
Let $\mathbb G$ be a graded Lie group with homogeneous dimension $Q$. In this paper, we study the Cauchy problem for a semilinear hypoelliptic damped wave equation involving a positive Rockland operator $\mathcal{R}$ of homogeneous degree $\nu\geq 2$
Externí odkaz:
http://arxiv.org/abs/2408.05598
Autor:
Ficek, Filip, Maliborski, Maciej
We propose a systematic approach of analysing the complex structure of time-periodic solutions to the cubic wave equation on interval with Dirichlet boundary conditions first reported in arXiv:2407.16507. Our results complement previous rigorous exis
Externí odkaz:
http://arxiv.org/abs/2408.05158