Chapter 1 Elliptic equations with anisotropic nonlinearity and nonstandard growth conditions

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Blow-up for parabolic and hyperbolic problems with variable exponents (2009, background): “2), with a(x) < 0, and 1 < p(x) < 2 arise in the mathematical models which describe the processes of absorption, see [1], [2] and [3] for the questions of existence, uniqueness and localization of solutions.”
Wave Equation with p(x,t) - Laplacian and Damping Term: Existence and Blow-up (2011, background): “, [5, 6, 8, 35, 36] ) and the further references therein).”