ترغب بنشر مسار تعليمي؟ اضغط هنا

Blowup behavior of strongly perturbed wave equations

308   0   0.0 ( 0 )
 نشر من قبل David Wallauch
 تاريخ النشر 2020
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We study the blowup behavior of a class of strongly perturbed wave equations with a focusing supercritical power nonlinearity in three spatial dimensions. We show that the ODE blowup profile of the unperturbed equation still describes the asymptotics of stable blowup. As a consequence, stable ODE-type blowup is seen to be a universal phenomenon that exists in a large class of semilinear wave equations.

قيم البحث

اقرأ أيضاً

We study the blowup behavior for the focusing energy-supercritical semilinear wave equation in 3 space dimensions without symmetry assumptions on the data. We prove the stability of the ODE blowup profile.
122 - Lei Zhang 2008
We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of Bartolucci-Chen-Lin-Tarantello it is proved that the profile of the solutions differs from global solutions of a Liouville type equation only by a uniformly bounded term. The present paper improves their result and establishes an expansion of the solutions near the blowup points with a sharp error estimate.
107 - Yan Lv , A. J. Roberts 2011
An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation u u_{tt}+u_t=D u+f(u)+ u^alphadot{W} on an open bounded domain $DsubsetR^n$,, $1leq nleq 3$,. Here $ u>0 $ is a small parameter characterising the singular perturbation, and $ u^alpha$,, $0leq alphaleq 1/2$,, parametrises the strength of the noise. Some scaling transformations and the martingale representation theorem yield the following effective approximation for small $ u$, u_t=D u+f(u)+ u^alphadot{W} to an error of $ord{ u^alpha}$,.
We consider co-rotational wave maps from the $(1+d)$-dimensional Minkowski space into the $d$-sphere for $dgeq 3$ odd. This is an energy-supercritical model which is known to exhibit finite-time blowup via self-similar solutions. Based on a method de veloped by the second author and Schorkhuber, we prove the asymptotic nonlinear stability of the ground-state self-similar solution.
We establish Strichartz estimates for the radial energy-critical wave equation in 5 dimensions in similarity coordinates. Using these, we prove the nonlinear asymptotic stability of the ODE blowup in the energy space.
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