GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO THE DOUBLE NONLINEAR POROUS MEDIUM EQUATION
Sabitbek B. Torebek B.T.
March 2024American Institute of Mathematical Sciences
Discrete and Continuous Dynamical Systems- Series A
2024#44Issue 3743 - 767 pp.
In this study, we examine a double nonlinear porous medium equation subject to a novel nonlinearity condition within a bounded domain. First, we introduce the blow-up solution for the problem under consideration for the negative initial energy. By introducing a set of potential wells, we construct invariant sets of solutions for the double nonlinear porous medium equation. For subcritical and critical initial energy scenarios, we derive the global existence and asymptotic behavior of weak solutions, as well as blow-up phenomena occurring within a finite time for the positive solution to the double nonlinear porous medium equation.
blow-up , Blow-up , global existence , p-Laplacian , porous medium equation
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School of Mathematical Sciences, Queen Mary University of London, United Kingdom
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium
School of Mathematical Sciences
Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
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