ترغب بنشر مسار تعليمي؟ اضغط هنا

Lifespan estimates for semilinear wave equations with space dependent damping and potential

109   0   0.0 ( 0 )
 نشر من قبل Mengyun Liu
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this work, we investigate the influence of general damping and potential terms on the blow-up and lifespan estimates for energy solutions to power-type semilinear wave equations. The space-dependent damping and potential functions are assumed to be critical or short range, spherically symmetric perturbation. The blow up results and the upper bound of lifespan estimates are obtained by the so-called test function method. The key ingredient is to construct special positive solutions to the linear dual problem with the desired asymptotic behavior, which is reduced, in turn, to constructing solutions to certain elliptic eigenvalue problems.



قيم البحث

اقرأ أيضاً

176 - Mengyun Liu 2021
In this work, we investigate the problem of finite time blow up as well as the upper bound estimates of lifespan for solutions to small-amplitude semilinear wave equations with time dependent damping and potential, and mixed nonlinearities $c_1 |u_t| ^p+c_2 |u|^q$, posed on asymptotically Euclidean manifolds, which is related to both the Strauss conjecture and the Glassey conjecture.
57 - Ning-An Lai , Ziheng Tu 2019
It is believed or conjectured that the semilinear wave equations with scattering space dependent damping admit the Strauss critical exponent, see Ikehata-Todorova-Yordanov cite{ITY}(the bottom in page 2) and Nishihara-Sobajima-Wakasugi cite{N2}(conje cture iii in page 4). In this work, we are devoted to showing the conjecture is true at least when the decay rate of the space dependent variable coefficients before the damping is larger than 2. Also, if the nonlinear term depends only on the derivative of the solution, we may prove the upper bound of the lifespan is the same as that of the solution of the corresponding problem without damping. This shows in another way the lqlq hyperbolicity of the equation.
In this paper we study the initial boundary value problem for two-dimensional semilinear wave equations with small data, in asymptotically Euclidean exterior domains. We prove that if $1<ple p_c(2)$, the problem admits almost the same upper bound of the lifespan as that of the corresponding Cauchy problem, only with a small loss for $1<ple 2$. It is interesting to see that the logarithmic increase of the harmonic function in $2$-D has no influence to the estimate of the upper bound of the lifespan for $2<ple p_c(2)$. One of the novelties is that we can deal with the problem with flat metric and general obstacles (bounded and simple connected), and it will be reduced to the corresponding problem with compact perturbation of the flat metric outside a ball.
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 new critical exponent $p=p_{mathrm{crit}}(n,gamma):=1+frac{4 }{n+2gamma}$ for some $gammain(0,frac{n}{2})$ and low dimensions in the framework of Soblev spaces of negative order. Precisely, global (in time) existence of small data Sobolev solutions of lower regularity is proved for $p>p_{mathrm{crit}}(n,gamma)$, and blow-up of weak solutions in finite time even for small data if $1<p<p_{mathrm{crit}}(n,gamma)$. Furthermore, in order to more accurately describe the blow-up time, we investigate sharp upper bound and lower bound estimates for the lifespan in the subcritical case.
101 - Taeko Yamazaki 2018
This paper is concerned with the initial value problem for semilinear wave equation with structural damping $u_{tt}+(-Delta)^{sigma}u_t -Delta u =f(u)$, where $sigma in (0,frac{1}{2})$ and $f(u) sim |u|^p$ or $u |u|^{p-1}$ with $p> 1 + {2}/(n - 2 sig ma)$. We first show the global existence for initial data small in some weighted Sobolev spaces on $mathcal R^n$ ($n ge 2$). Next, we show that the asymptotic profile of the solution above is given by a constant multiple of the fundamental solution of the corresponding parabolic equation, provided the initial data belong to weighted $L^1$ spaces.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا