Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type with Logarithmic Source

Authors : Carlos RAPOSO, Adriano CATTAİ, Octavio VERA, Ganesh CH GORAIN, Ducival PEREİRA

Pages : 112-128

Doi:10.36753/mathenot.1084371

View : 103 | Download : 171

Publication Date : 2023-09-02

Article Type : Research Paper

Abstract :This manuscript deals with global solution, polynomial stability and blow-up behavior at a finite time for the nonlinear system $$ \\left\\{ \\begin{array}{rcl} & u\`\` - \\Delta_{p} u + \\theta + \\alpha u\` = \\left\\vert u\\right\\vert ^{p-2}u\\ln \\left\\vert u\\right\\vert \\\\ &\\theta\` - \\Delta \\theta = u\` \\end{array} \\right. $$ where $\\Delta_{p}$ is the nonlinear $p$-Laplacian operator, $ 2 \\leq p < \\infty$. Taking into account that the initial data is in a suitable stability set created from the Nehari manifold, the global solution is constructed by means of the Faedo-Galerkin approximations. Polynomial decay is proven for a subcritical level of initial energy. The blow-up behavior is shown on an instability set with negative energy values.
Keywords : Global solution, blow up, thermoelastic system of p Laplacian type, logarithmic source

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