Abstract
The authors of this paper study a nonlinear viscoelastic equation with variable exponents. By using the Faedo-Galerkin method and embedding theory, the existence of weak solutions is given to the initial and boundary value problem under suitable assumptions.
Highlights
Let ⊂ RN (N ≥ ) be a bounded Lipschitz domain and < T < ∞
In the case when m, p are constants, there have been many results about the existence and blow-up properties of the solutions, we refer the readers to the bibliography given in [ – ]
Much attention has been paid to the study of mathematical models of electro-rheological fluids. These models include hyperbolic, parabolic or elliptic equations which are nonlinear with respect to gradient of the thought solution and with variable exponents of nonlinearity; see [ – ] and references therein
Summary
Let ⊂ RN (N ≥ ) be a bounded Lipschitz domain and < T < ∞. Consider the following nonlinear viscoelastic hyperbolic problem: In the case when m, p are constants, there have been many results about the existence and blow-up properties of the solutions, we refer the readers to the bibliography given in [ – ]. These models include hyperbolic, parabolic or elliptic equations which are nonlinear with respect to gradient of the thought solution and with variable exponents of nonlinearity; see [ – ] and references therein.
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