Naslov
Estimates on the mild solution of semilinear Cauchy problems and some notes on damped wave equations

Autori
Burazin, Krešimir ; Erceg, Marko

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
Chemnitz-Zagreb Workshop on Harmonic Analysis for PDE

Mjesto i datum
Chemnitz, Njemačka, 01.07.2014. - 05.07.2014

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
mild solution; semigroups; semilinear; wave equation

Sažetak
The existence (and uniqueness) results on mild solutions of the abstract semilinear Cauchy problems in Banach spaces are well known. Following the results of Tartar (2008) and Burazin (2008) in the case of decoupled hyperbolic systems, we give an alternative proof, which enables us to derive an estimate on the mild solution and its time of existence. The nonlinear term in the equation is allowed to be time-dependent. We discuss the optimality of the derived estimate by testing it on two examples: the semilinear heat equation that models dynamic deflection of an elastic membrane, and the semilinear Schrödinger equation with time-dependent nonlinearity, that appear in the modelling of numerous physical phenomena. In the second part of the talk it will be presented ongoing research based on the result of K. Veselić (2004) for abstract damped systems with fairly general operator coefficients (even some mixed-type equations are contained in this setting). The main idea is to better understand the notion of solution and possible get new results for some mixed-type equations.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA