ﻻ يوجد ملخص باللغة العربية
We are concerned with nonexistence results for a class of quasilinear parabolic differential problems with a potential in $Omegatimes(0,+infty)$, where $Omega$ is a bounded domain. In particular, we investigate how the behavior of the potential near the boundary of the domain and the power nonlinearity affect the nonexistence of solutions. Particular attention is devoted to the special case of the semilinear parabolic problem, for which we show that the critical rate of growth of the potential near the boundary ensuring nonexistence is sharp.
We bound the difference between solutions $u$ and $v$ of $u_t = aDelta u+Div_x f+h$ and $v_t = bDelta v+Div_x g+k$ with initial data $phi$ and $ psi$, respectively, by $Vert u(t,cdot)-v(t,cdot)Vert_{L^p(E)}le A_E(t)Vert phi-psiVert_{L^infty(R^n)}^{2r
We prove nonexistence of nontrivial, possibly sign changing, stable solutions to a class of quasilinear elliptic equations with a potential on Riemannian manifolds, under suitable weighted volume growth conditions on geodesic balls.
In this paper we are concerned with a class of elliptic differential inequalities with a potential in bounded domains both of $mathbf{R}^m$ and of Riemannian manifolds. In particular, we investigate the effect of the behavior of the potential at the
We study fractional parabolic equations with indefinite nonlinearities $$ frac{partial u} {partial t}(x,t) +(-Delta)^s u(x,t)= x_1 u^p(x, t),,, (x, t) in mathbb{R}^n times mathbb{R}, $$ where $0<s<1$ and $1<p<infty$. We first prove that all positive
We introduce a notion of quasilinear parabolic equations over metric measure spaces. Under sharp structural conditions, we prove that local weak solutions are locally bounded and satisfy the parabolic Harnack inequality. Applications include the para