Glasnik Matematicki, Vol. 54, No. 1 (2019), 179-209.

TIME DECAY ESTIMATES FOR WAVE EQUATIONS WITH TRANSMISSION AND BOUNDARY CONDITIONS

Krešo Mihalinčić

Faculty of Tourism and Hospitality Management, University of Rijeka, Primorska 42, 51410 Opatija, Croatia
e-mail: kresom@fthm.hr


Abstract.   Time decay estimates are derived for solutions of some initial value problems of wave propagation, based on the method of stationary phase. Solutions to three dimensional wave equation in wedges and one dimensional wave equation with a constant potential are shown to decay like t-1 and t-1/2, respectively. Dependencies of the results on initial data and physical implications are discussed.

2010 Mathematics Subject Classification.   35L05, 74S25, 35G16

Key words and phrases.   Partial differential equations, initial boundary value problem, mathematical physics, wave propagation, stationary phase, time decay


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DOI: 10.3336/gm.54.1.08


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