Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 194, pp. 110.
Estimates for mild solutions to semilinear Cauchy problems
Kresimir Burazin, Marko Erceg
Abstract:
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 timedependent.
We discuss the optimality of the derived estimate by testing it on three
examples: the linear heat equation, the semilinear heat equation that
models dynamic deflection of an elastic membrane, and the semilinear
Schrodinger equation with timedependent nonlinearity, that appear
in the modelling of numerous physical phenomena.
Submitted July 29, 2014. Published September 18, 2014.
Math Subject Classifications: 47A50, 47D06, 47J35, 35K58, 35Q55.
Key Words: Semigroup; abstract Cauchy problem; blowup; quenching time.
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Kresimir Burazin
Department of Mathematics, University of Osijek
Trg Ljudevita Gaja 6, Osijek, Croatia
email: kburazin@mathos.hr


Marko Erceg
Department of Mathematics
Faculty of Science, University of Zagreb
Bijenicka cesta 30, Zagreb, Croatia
email: maerceg@math.hr

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