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Estimates on the mild solution of semilinear Cauchy problems and some notes on damped wave equations (CROSBI ID 625951)

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Burazin, Krešimir ; Erceg, Marko Estimates on the mild solution of semilinear Cauchy problems and some notes on damped wave equations // Chemnitz-Zagreb Workshop on Harmonic Analysis for PDE Chemnitz, Njemačka, 01.07.2014-05.07.2014

Podaci o odgovornosti

Burazin, Krešimir ; Erceg, Marko

engleski

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

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.

mild solution; semigroups; semilinear; wave equation

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Podaci o prilogu

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Podaci o skupu

Chemnitz-Zagreb Workshop on Harmonic Analysis for PDE

predavanje

01.07.2014-05.07.2014

Chemnitz, Njemačka

Povezanost rada

Matematika