O problema que vamos estudar neste trabalho é motivado pela dinâmica de equações diferenciais não autônomas. Vamos estabelecer a existência e unicidade de solução para uma classe de equaçõoes parabólicas semilineares com ...

Neste trabalho, analisaremos o problema de boa colocação do problema de valor inicial para a equação semilinear do calor. Mostraremos a existência de solução global mild, quando o dado inicial u_0 pertence ao espaço L^( ...

Let Omega be a bounded smooth domain in R-N. We consider the problem u(t) = Delta u + V(x)u(P) in Omega x [0, T), with Dirichlet boundary conditions u = 0 on partial derivative Omega x [0, T) and initial datum u (x, 0) = ...

The paper is devoted to the classification of entire solutions to the Cahn–Hilliard equation −u = u −u3 −δ in RN , with particular interest in those solutions whose nodal set is either bounded or contained in a cylinder. ...

We construct a periodic solution to the semilinear heat equation with power nonlinearity, in one space dimension, which blows up in finite time T only at one blow-up point. We also give a sharp description of its blow-up ...

The goal of this note is to study the asymptotic behavior of positive solutions for a class of semilinear elliptic equations which can be realized as minimizers of their energy functionals. This class includes the Fisher-KPP ...