Behaviour of solutions to as p → +∞
Bi-spaces global attractors in abstract parabolic equations
An abstract semilinear parabolic equation in a Banach space X is considered. Under general assumptions on nonlinearity this problem is shown to generate a bounded dissipative semigroup on . This semigroup possesses an -global attractor that is closed, bounded, invariant in , and attracts bounded subsets of in a ’weaker’ topology of an auxiliary Banach space Z. The abstract approach is finally applied to the scalar parabolic equation in Rⁿ and to the partly dissipative system.
Blow-up behaviour of one-dimensional semilinear parabolic equations
Blow-up rate for parabolic problems with nonlocal source and boundary flux.
Blow-up versus global existence of solutions to aggregation equations
A class of nonlinear viscous transport equations describing aggregation phenomena in biology is considered. General conditions on an interaction potential are obtained which lead either to the existence or to the nonexistence of global-in-time solutions.
Borel summable solutions of the Burgers equation
We give necessary and sufficient conditions for the formal power series solutions to the initial value problem for the Burgers equation to be convergent or Borel summable.
Boundary value problems for the diffusion equation with piecewise continuous time delay.
Bounded solutions of nonlinear parabolic equations with time delay.