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) = ...

We obtain existence of asymptotically stable nonconstant equilibrium solutions for semilinear parabolic equations with nonlinear boundary conditions on small domains connected by thin channels. We prove the convergence of ...

We obtain existence of asymptotically stable nonconstant equilibrium solutions for semilinear parabolic equations with nonlinear boundary conditions on small domains connected by thin channels. We prove the convergence of ...

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural ...

In this paper, we study the behavior of the solutions of nonlinear parabolic problems posed in a domain that degenerates into a line segment (thin domain) which has an oscillating boundary. We combine methods from linear ...