An initial value problem is considered for the nonlinear dissipative wave equation containing the $ p(x) $-bi-Laplacian operator. For this problem, sufficient conditions for the blow-up with nonpositive initial energy of a generalized solution are obtained in finite time where a wide variety of techniques are used.
Citation: Khaled Zennir, Abderrahmane Beniani, Belhadji Bochra, Loay Alkhalifa. Destruction of solutions for class of wave $ p(x)- $bi-Laplace equation with nonlinear dissipation[J]. AIMS Mathematics, 2023, 8(1): 285-294. doi: 10.3934/math.2023013
An initial value problem is considered for the nonlinear dissipative wave equation containing the $ p(x) $-bi-Laplacian operator. For this problem, sufficient conditions for the blow-up with nonpositive initial energy of a generalized solution are obtained in finite time where a wide variety of techniques are used.
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