ترغب بنشر مسار تعليمي؟ اضغط هنا

On Uniqueness of Boundary Blow-up Solutions of a Class of Nonlinear Elliptic Equations

173   0   0.0 ( 0 )
 نشر من قبل Seick Kim
 تاريخ النشر 2007
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We study boundary blow-up solutions of semilinear elliptic equations $Lu=u_+^p$ with $p>1$, or $Lu=e^{au}$ with $a>0$, where $L$ is a second order elliptic operator with measurable coefficients. Several uniqueness theorems and an existence theorem are obtained.



قيم البحث

اقرأ أيضاً

152 - H.Chen , H. Hajaiej 2016
In this paper, we study existence of boundary blow-up solutions for elliptic equations involving regional fractional Laplacian. We also discuss the optimality of our results.
We are concerned with the focusing $L^2$-critical nonlinear Schrodinger equations in $mathbb{R}^d$ for $d=1,2$. The uniqueness is proved for a large energy class of multi-bubble blow-up solutions, which converge to a sum of $K$ pseudo-conformal blow- up solutions particularly with low rate $(T-t)^{0+}$, as $tto T$, $1leq K<infty$. Moreover, we also prove the uniqueness in the energy class of multi-solitons which converge to a sum of $K$ solitary waves with convergence rate $(1/t)^{2+}$, as $tto infty$. The uniqueness class is further enlarged to contain the multi-solitons with even lower convergence rate $(1/t)^{frac 12+}$ in the pseudo-conformal space. The proof is mainly based on the pseudo-conformal invariance and the monotonicity properties of several functionals adapted to the multi-bubble case, the latter is crucial towards the upgradation of the convergence to the fast exponential decay rate.
In this short note, we present a construction for the log-log blow up solutions to focusing mass-critical stochastic nonlinear Schroidnger equations with multiplicative noises. The solution is understood in the sense of controlled rough path as in cite{SZ20}.
274 - Rupert L. Frank , Tobias Konig , 2021
We describe the asymptotic behavior of positive solutions $u_epsilon$ of the equation $-Delta u + au = 3,u^{5-epsilon}$ in $Omegasubsetmathbb{R}^3$ with a homogeneous Dirichlet boundary condition. The function $a$ is assumed to be critical in the sen se of Hebey and Vaugon and the functions $u_epsilon$ are assumed to be an optimizing sequence for the Sobolev inequality. Under a natural nondegeneracy assumption we derive the exact rate of the blow-up and the location of the concentration point, thereby proving a conjecture of Brezis and Peletier (1989). Similar results are also obtained for solutions of the equation $-Delta u + (a+epsilon V) u = 3,u^5$ in $Omega$.
We show that blow up of solutions with arbitrary positive initial energy of the Cauchy problem for the abstract wacve eqation of the form $Pu_{tt}+Au=F(u) (*)$ in a Hilbert space, where $P,A$ are positive linear operators and $F(cdot)$ is a continuo usly differentiable gradient operator can be obtained from the result of H.A. Levine on the growth of solutions of the Cauchy problem for (*). This result is applied to the study of inital boundary value problems for nonlinear Klein-Gordon equations, generalized Boussinesq equations and nonlinear plate equations. A result on blow up of solutions with positive initial energy of the initial boundary value problem for wave equation under nonlinear boundary condition is also obtained.
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