相关论文: F-stability, entropy and energy gap for supercriti…
This paper is concerned with blow-up solutions of the 4-dimensional energy critical heat equation $u_t=\Delta u + u^3$. Our main result is to show that the existence of type II blowup solutions, and…
We consider the nonlinear heat equation $u_t-\Delta u =|u|^p+b |\nabla u|^q$ in $(0,\infty)\times \R^n$, where $n\geq 1$, $p>1$, $q\geq 1$ and $b>0$. First, we focus our attention on positive solutions and obtain an optimal Fujita-type…
Refined structures of blowup for non-collapsing maximal solution to a semilinear parabolic equation are studied. We will prove that the blowup set is empty for non-collapsing blowing-up in subcritical case, and all finite time…
The asymptotic bahavior of blowup solutions to the Fujita type heat equation $u_t=\Delta u+|u|^{p-1}u$ is studied. This equation admits the ODE type blowup given by $u(x,t)=(p-1)^\frac{1}{p-1}(T-t)^{-\frac{1}{p-1}}$. It is known that…
We consider co--rotational wave maps from (3+1) Minkowski space into the three--sphere. This is an energy supercritical model which is known to exhibit finite time blow up via self-similar solutions. The ground state self--similar solution…
We study monotone finite difference approximations for a broad class of reaction-diffusion problems, incorporating general symmetric L\'evy operators. By employing an adaptive time-stepping discretization, we derive the discrete Fujita…
We consider the semilinear wave equation \[ \partial_t^2 \psi-\Delta \psi=|\psi|^{p-1}\psi \] for $1<p\leq 3$ with radial data in $\R^{3}$. This equation admits an explicit spatially homogeneous blow up solution $\psi^T$ given by $$…
We study the semilinear wave equation \[ \partial_t^2 \psi-\Delta \psi=|\psi|^{p-1}\psi \] for $p > 3$ with radial data in three spatial dimensions. There exists an explicit solution which blows up at $t=T>0$ given by \[ \psi^T(t,x)=c_p…
The aim of this paper is to refine some results concerning the blow-up of solutions of the exponential reaction-diffusion equation. We consider solutions that blow-up in finite time, but continue to exist as weak solutions beyond the…
In this paper, we obtain a blow-up result for solutions to a semi-linear wave equation with scale-invariant dissipation and mass and power non-linearity, in the case in which the model has a "wave like" behavior. In order to achieve this…
The behaviour of solutions for a non-linear diffusion problem is studied. A subordination principle is applied to obtain the variation of parameters formula in the sense of Volterra equations, which leads to the integral representation of a…
In this paper we consider the nonlinear Schr\"o\-din\-ger equation $i u_t +\Delta u +\kappa |u|^\alpha u=0$. We prove that if $\alpha <\frac {2} {N}$ and $\Im \kappa <0$, then every nontrivial $H^1$-solution blows up in finite or infinite…
This paper studies a nonlinear plate equation with internal fractional damping and a time-delay term, driven by a polynomial-type nonlinear source. Such a model arises naturally in the description of viscoelastic and feedback-controlled…
In this work, we are interested on the study of the Fujita exponent and the meaning of the blow-up for the Fractional Cauchy problem with the Hardy potential, namely, \begin{equation*} u_t+(-\Delta)^s…
We are concerned with blow-up solutions of the 5-dimensional energy critical heat equation $u_t=\Delta u + | u |^{\frac{4}{3}}u$. Our main result is to show that the existence of type 2 solutions blows up at 2 points with 2 different…
We investigate a suspension bridge model described by a nonlinear plate equation incorporating internal fractional damping and infinite memory effects. The system also includes a nonlinear source term that may induce instability. Using…
This paper is devoted to the study of the regularity of solutions to some systems of reaction--diffusion equations, with reaction terms having a subquadratic growth. We show the global boundedness and regularity of solutions, without…
We consider a special class of infinite energy solutions to the inviscid incompressible porous medium equations (IPM), introduced in Castro-C\'ordoba-Gancedo-Orive [9]. The (IPM) equations then reduce to a one-dimensional nonlocal nonlinear…
We analyze a reaction-diffusion system on $\mathbb{R}^{N}$ which models the dispersal of individuals between two exchanging environments for its diffusive component and incorporates a Fujita-type growth for its reactive component. The…
We study the stability of recently constructed self-similar blow-up solutions to the incompressible Euler equation. A consequence of our work is the existence of finite-energy $C^{1,\alpha}$ solutions that become singular in finite time in…