ترغب بنشر مسار تعليمي؟ اضغط هنا

Global behaviors of defocusing semilinear wave equations

86   0   0.0 ( 0 )
 نشر من قبل Shiwu Yang
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English
 تأليف Shiwu Yang




اسأل ChatGPT حول البحث

In this paper, we investigate the global behaviors of solutions to defocusing semilinear wave equations in $mathbb{R}^{1+d}$ with $dgeq 3$. We prove that in the energy space the solution verifies the integrated local energy decay estimates for the full range of energy subcritical and critical power. For the case when $p>1+frac{2}{d-1}$, we derive a uniform weighted energy bound for the solution as well as inverse polynomial decay of the energy flux through hypersurfaces away from the light cone. As a consequence, the solution scatters in the energy space and in the critical Sobolev space for $p$ with an improved lower bound. This in particular extends the existing scattering results to higher dimensions without spherical symmetry.



قيم البحث

اقرأ أيضاً

163 - Dongyi Wei , Shiwu Yang 2020
In this paper, we study the asymptotic decay properties for defocusing semilinear wave equations in $mathbb{R}^{1+2}$ with pure power nonlinearity. By applying new vector fields to null hyperplane, we derive improved time decay of the potential energ y, with a consequence that the solution scatters both in the critical Sobolev space and energy space for all $p>1+sqrt{8}$. Moreover combined with Br{e}zis-Gallouet-Wainger type of logarithmic Sobolev embedding, we show that the solution decays pointwise with sharp rate $t^{-frac{1}{2}}$ when $p>frac{11}{3}$ and with rate $t^{ -frac{p-1}{8}+epsilon }$ for all $1<pleq frac{11}{3}$. This in particular implies that the solution scatters in energy space when $p>2sqrt{5}-1$.
191 - Dongyi Wei , Shiwu Yang 2020
This paper is devoted to the study of asymptotic behaviors of solutions to the one-dimensional defocusing semilinear wave equation. We prove that finite energy solution tends to zero in the pointwise sense, hence improving the averaged decay of Lindb lad and Tao. Moreover, for sufficiently localized data belonging to some weighted energy space, the solution decays in time with an inverse polynomial rate. This confirms a conjecture raised in the mentioned work. The results are based on new weighted vector fields as multipliers applied to regions enclosed by light rays. The key observation for the first result is an integrated local energy decay for the potential energy, while the second result relies on a type of weighted Gagliardo-Nirenberg inequality.
97 - Dongyi Wei , Shiwu Yang 2021
By introducing new weighted vector fields as multipliers, we derive quantitative pointwise estimates for solutions of defocusing semilinear wave equation in $mathbb{R}^{1+3}$ with pure power nonlinearity for all $1<pleq 2$. Consequently, the solution vanishes on the future null infinity and decays in time polynomially for all $sqrt{2}<pleq 2$. This improves the uniform boundedness result of the second author when $frac{3}{2}<pleq 2$.
101 - Mengyun Liu , Chengbo Wang 2018
We study the global existence of solutions to semilinear wave equations with power-type nonlinearity and general lower order terms on $n$ dimensional nontrapping asymptotically Euclidean manifolds, when $n=3, 4$. In addition, we prove almost global e xistence with sharp lower bound of the lifespan for the four dimensional critical problem.
135 - Yige Bai , Mengyun Liu 2018
We study the global existence of solutions to semilinear damped wave equations in the scattering case with derivative power-type nonlinearity on (1+3) dimensional nontrapping asymptotically Euclidean manifolds. The main idea is to exploit local energ y estimate, together with local existence to convert the parameter $mu$ to small one.
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