Well-posedness of non-autonomous semilinear systems

H-global well-posedness for semilinear wave equations

We consider the Cauchy problem for semilinear wave equations in Rn with n 3. Making use of Bourgain’s method in conjunction with the endpoint Strichartz estimates of Keel and Tao, we establish the Hs-global well-posedness with s < 1 of the Cauchy problem for the semilinear wave equation. In doing so a number of nonlinear a priori estimates is established in the framework of Besov spaces. Our me...

Well-posedness of Hybrid Systems

Well–posedness and Asymptotic Behaviour for a Non-classical and Non-autonomous Diffusion Equation with Delay

In this paper, it is analyzed a non-classical non-autonomous diffusion equation with delay. First, the well-posedness and the existence of a local solution is proved by using a fixed point theorem. Then, the existence of solutions defined globally in future is ensured. The asymptotic behaviour of solutions is analyzed within the framework of pullback attractors as it has revealed a powerful the...

Well{posedness of Stiff Hyperbolic Systems

The theory of stii well{posedness of initial value problems for hyperbolic systems with large relaxation terms is reviewed. Furthermore, an asymptotic expansion of solutions with respect to the relaxation parameter is presented. Finally, the theory is illustrated with an example and an outlook concerning boundary value problems is given.

Well{posedness and Asymptotic Behaviour of Non{autonomous Linear Evolution Equations

We review results on the existence and the long term behaviour of non– autonomous linear evolution equations. Emphasis is put on recent results on the asymptotic behaviour using a semigroup approach.