Biharmonic equation of energy decay estimates _369

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Biharmonic equation of energy decay estimates
 
 
Number (both known function ) defined in the integral . By ( 10) and type (17 ) ~ (19) to know : 246 Changchun University of Technology ( Natural Science) Vol 27 E (o) a I printed . Currency. Currency dA-J. z-J. - State z2 a JLoJL0JL0. a. adzz-JL0 Ⅲ dzz (22) JLoJLo on who can use a (O), its derivatives and other points that are known to function with the . Known function , so in equation ( 22) only estimated the final points. ≤ a J-L. . - state. zz-J-L. . zzdzz one hundred and eleven (△), 1dA-R (△). . . . dA a △. . . . dA-R △. . . . dA-RI △. . . . dA: JRI △. 1dA: JRJ1 + J2 (23) repeated use of integration by parts and boundary conditions, was : J1 a J,. △. . dA = JRI. m. . dA-l (. m). . dA-JRJ-. Throw dA + J-. Canada . . dA = A I. (.。). , DA-JR-I. . Stare dA-I. Port l. . dA ≤ JRJR. Bar dA +. dA + dA + bar bar bar dA + dA ≤ bar ,You are not allowed to view links. Register or Login, dA a 1E, (O) + if. . . dA A - E '(0) + special J-, tincture . dA + lost J-2dA-data (24) Application of the arithmetic mean inequality and the inequality I △ I ≤ 2 (1 + process 2) ≤ 2. . By J2 = a I △. 1dA ≤ JR tie I △ IdA + dA ≤ currency dA + dA = A E, (o) + lost J-. dA (25) noted. - known function and a E, (O) boundedness , combined type (22) ~ type (25) know that E (O) Bu sector the right shows