Lp estimates of solutions of some partial differential equations |
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| Affiliation: | 1. Department of Mathematics, Wayne State University, Detroit, MI 48022, USA;2. Department of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, PR China;1. Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland;2. Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warsaw, Poland;1. Department of Industrial Engineering and Mathematical Sciences, Marche Polytechnic University, Via Brecce Bianche, 06131, Ancona, Italy;2. Department of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123, Perugia, Italy;1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada;2. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Prague 1, Czech Republic;3. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People’s Republic of China;1. Ahi Evran University, Department of Mathematics, Kirsehir, Turkey;2. Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, F. Agayev St. 9, Baku, AZ 1141, Azerbaijan;3. Baku State Univ., Dept. Math. Anal., Baku, AZ 1141, Azerbaijan;4. Dipartimento di Matematica, Università di Catania, Viale A. Doria, 6, 95125 Catania, Italy |
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| Abstract: | The author is concerned with the long time asymptotic behaviors of the global weak solutions of some nonlinear evolution equations. First of all, he derives some uniform L1 and L∞ upper bounds for the solutions, under some mild conditions. Then, by applying the well-known Fourier splitting method and the L1 estimates, he asserts the L2 decay estimates of the solutions. The rates of decay are sharp in the sense that the integral of the initial data over is nonzero. |
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