000118705 001__ 118705 000118705 005__ 20240319080949.0 000118705 0247_ $$2doi$$a10.3390/math10173128 000118705 0248_ $$2sideral$$a129847 000118705 037__ $$aART-2022-129847 000118705 041__ $$aeng 000118705 100__ $$0(orcid)0000-0003-2453-7841$$aAbadias, Luciano$$uUniversidad de Zaragoza 000118705 245__ $$aAsymptotic behavior for the discrete in time heat equation 000118705 260__ $$c2022 000118705 5060_ $$aAccess copy available to the general public$$fUnrestricted 000118705 5203_ $$aIn this paper, we investigate the asymptotic behavior and decay of the solution of the discrete in time N-dimensional heat equation. We give a convergence rate with which the solution tends to the discrete fundamental solution, and the asymptotic decay, both in Lp(RN). Furthermore, we prove optimal L2-decay of solutions. Since the technique of energy methods is not applicable, we follow the approach of estimates based on the discrete fundamental solution which is given by an original integral representation and also by MacDonald’s special functions. As a consequence, the analysis is different to the continuous in time heat equation and the calculations are rather involved. 000118705 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000118705 590__ $$a2.4$$b2022 000118705 592__ $$a0.446$$b2022 000118705 591__ $$aMATHEMATICS$$b23 / 329 = 0.07$$c2022$$dQ1$$eT1 000118705 593__ $$aComputer Science (miscellaneous)$$c2022$$dQ2 000118705 593__ $$aMathematics (miscellaneous)$$c2022$$dQ2 000118705 593__ $$aEngineering (miscellaneous)$$c2022$$dQ2 000118705 594__ $$a3.5$$b2022 000118705 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000118705 700__ $$aAlvarez, Edgardo 000118705 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000118705 773__ $$g10, 17 (2022), 3128 [22 pp.]$$pMathematics (Basel)$$tMathematics$$x2227-7390 000118705 8564_ $$s947174$$uhttps://zaguan.unizar.es/record/118705/files/texto_completo.pdf$$yVersión publicada 000118705 8564_ $$s1971344$$uhttps://zaguan.unizar.es/record/118705/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000118705 909CO $$ooai:zaguan.unizar.es:118705$$particulos$$pdriver 000118705 951__ $$a2024-03-18-12:54:18 000118705 980__ $$aARTICLE