Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 531, Issue 2, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2023.127848
Keywords
Fourth order partial differential operators; Plate equation; Carleman estimate
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In this paper, a fundamental inequality for a fourth order partial differential operator is established, and using this inequality, some Carleman estimates for the operator with suitable boundary conditions are proved. As an application, a resolvent estimate for the operator is obtained, which implies a log-type stabilization result for the plate equation.
In this paper, we establish a fundamental inequality for fourth order partial differential operator P-=(triangle)alpha partial derivative(s)+beta partial derivative(ss)+Delta(2) (alpha, beta is an element of R) with an abstract exponential-type weight function. Such kind of weight functions including not only the regular weight functions but also the singular weight functions. Using this inequality we are able to prove some Carleman estimates for the operator P with some suitable boundary conditions in the case of beta<0 or alpha not equal 0,beta=0. As application, we obtain a resolvent estimate for P, which can imply a log-type stabilization result for the plate equation with clamped boundary conditions or hinged boundary conditions.
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