Local existence and nonexistence of global solutions for a plate equation with time delay
1Dicle University, Department of Mathematics, 21280 Diyarbakır, Turkey
Sigma J Eng Nat Sci 2021; 39(): 23-32 DOI: 10.14744/sigma.2021.00038
Abstract
In this article, we study a plate equation with frictional damping, nonlinear source and time delay. Firstly, we establish the local existence by using the semigroup theory. Then, under suitable conditions, we prove the nonexistence of global solutions for positive initial energy. Time delays often appear in many practical problems such as thermal, economic phenomena, biological, chemical, physical, electrical engineering systems, mechanical applications and medicine.
Keywords: Local existence, nonexistence, plate equation, time delay.