We consider the blow-up of solutions for a semilinear reaction diffusion equation with exponential reaction term. It is know that certain solutions that can be continued beyond the blow-up time possess a nonconstant selfsimilar blow-up profile. Our aim is to find the final time blow-up profile for such solutions. The proof is based on general ideas using semigroup estimates. The same approach w...

We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions tend to zero or blow up in a finite time. We also give the asymptotic behavior of solutions which tend to zero as t→ ∞. Finally, we obtain the asymptotic behavior near the blow-up time of certain blow-up solutions and describe their blow-up set.

Abstract We consider the semilinear heat equation with Sobolev subcritical power nonlinearity in dimension $N=2$, and $u(x,t)$ a solution that blows up finite time $T$. Given non-isolated blow-up point $a$, we assume Taylor expansion of near $(a,T)$ obeys some degenerate situation labeled by even integer $m(a)\ge 4$. If have sequence $a_n \to a$ as $n\to \infty $, show after change coordinates ...

In this paper we consider the inhomogeneous nonlinear Schrödinger (INLS) equation $$\begin{aligned} i \partial _t u +\Delta +|x|^{-b} |u|^{2\sigma }u = 0, \,\,\, x \in {\mathbb {R}}^N \end{aligned}$$ with $$N\ge 3$$ . We focus on intercritical case, where scaling invariant Sobolev index $$s_c=\frac{N}{2}-\frac{2-b}{2\sigma }$$ satisfies $$0<s_c<1$$ a previous work, for radial initial data in $$...

In this paper, a singular non-Newton polytropic filtration equation under the initial-boundary value condition is revisited. The finite time blow-up results were discussed when initial energy E(u0) was subcritical (E(u0)&lt;d), critical (E(u0)=d), and supercritical (E(u0)&gt;d), with d being potential depth by using well method some differential inequalities. goal of paper to give result if ind...

We revisit the finite time blow-up for fourth-order Schrödinger equation with focusing inhomogeneous nonlinearity −|x|−2|u|4nu. By exploiting localized virial estimates and spatial decay of nonlinearity, we prove non-radial solutions negative energy. Our result is first one dealing existence to equations.