On the long time behaviour of solutions of a class of autonomous reaction-diffusion systems.
On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis
We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller-Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.
On the role of the equal-area condition in internal layer stationary solutions to a class of reaction-diffusion systems.
On the solution of reaction-diffusion equations with double diffusivity.
On the speed of spread for fractional reaction-diffusion equations.
On the structure of spectra of travelling waves.
On the uniform boundedness of the solutions of systems of reaction-diffusion equations.
Optimal control and numerical adaptivity for advection–diffusion equations
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from splitting...
Optimal control and numerical adaptivity for advection–diffusion equations
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the Lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from...
Optimal interface error estimates for the mean curvature flow
Optimal Tikhonov approximation for a sideways parabolic equation.