Domains of attraction of equilibria and monotonicity properties of convergent trajectories in parabolic systems admitting strong comparison principle.
Realization of any finite jet in a scalar semilinear parabolic equation on the ball in
Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
We consider three types of semilinear second order PDEs on a cylindrical domain , where is a bounded domain in , . Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of is reserved for time , the third type is an elliptic equation with a singled out unbounded variable . We discuss the asymptotic behavior, as , of solutions which are defined and bounded on .
Group Actions on Strongly Monotone Dynamical Systems.
Imbedding vector fields in scalar parabolic Dirichlet
Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball.
Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations
We prove a Liouville type theorem for sign-changing radial solutions of a subcritical semilinear heat equation . We use this theorem to derive a priori bounds, decay estimates, and initial and final blow-up rates for radial solutions of rather general semilinear parabolic equations whose nonlinearities have a subcritical polynomial growth. Further consequences on the existence of steady states and time-periodic solutions are also shown.
Realization of the dynamics of ODE's in scalar parabolic PDE's
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations
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