WSEAS Transactions on Fluid Mechanics
Print ISSN: 1790-5087, E-ISSN: 2224-347X
Volume 18, 2023
Blow-up and Bounds of Solutions for a Class of Semi-Linear PseudoParabolic Equations with $$p$$(. )-Laplacian Viscoelastic Term
Authors: ,
Abstract: In a bounded domain subject to Dirichlet boundary conditions, this paper discusses the phenomenon of finite time blow-up of solutions for a particular class of evolution equations that affects the pseudo -Laplacian viscoelastic term. We give the equation by: $$u_t-Δu-\int_{0}^{t} g(t-s)Δ_{p}(x)u(x,s)ds=|u|^{q(x)-2}u$$. Our findings show that, regardless of the initial energy and sizable initial values, the classical solutions of this equation blow-up in finite time in two cases. Subject to certain conditions on p, q, g, and the initial given data, we have established a new criterion for blow-up and provided lower and upper bounds on the solutions if blow-up occurs.
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Keywords: Pseudo-parabolic equation, p(.)-Laplacian viscoelastic term, memory term, blow-up time, bounds of the blow-up time, critical exponents, variable nonlinearity
Pages: 157-172
DOI: 10.37394/232013.2023.18.16