In this paper, we consider a nonlinear p .x/Laplacian equation with
delay of time and variable exponents. Firstly, we prove the blow up of
solutions. Then, by applying an integral inequality due to Komornik, we
obtain the decay result. These results improve and extend earlier
results in the literature.
In this paper, we consider the following Timoshenko equationassociated with initial and Dirichlet boundary conditions. We prove the non-existence of solutions with positive and negative initial energy.2010 Mathematics Subject Classification. Primary: 35A01.1 2 Non-existence of solutions for a Timoshenko equations with weak. . .
In this work, we study a plate equation with time delay in the velocity, frictional damping, and logarithmic source term. Firstly, we obtain the local and global existence of solutions by the logarithmic Sobolev inequality and the Faedo-Galerkin method. Moreover, we prove the stability and nonexistence results by the perturbed energy and potential well methods.
This paper is concerned with a stability result for a Kirchhoff beam equation with variable exponents and time delay. The exponential and polynomial stability results are proved based on Komornik's inequality.
In this article, we deal with a logarithmic wave equation with strong damping and delay. Firstly, we prove the local existence by utilizing the semigroup theory. Later, we obtain the global existence of solutions by using the well‐depth method. Moreover, under appropriate assumptions on the weight of the delay and that of strong damping, we get the exponential decay.
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