Boundedness of global solutions of nonlinear diffusion equations
Copyright policy )Boundedness of global solutions of nonlinear diffusion equations
This paper deals with large time behaviour of solutions of Dirichlet- initial value problems for the equation \(u_ t=\Delta(| u|^{m- 1}u)+f(u)\) when \(f\) grows superlinearly. In particular the question of global existence without uniform a priori bounds is examined. The case when \(m=1\) and \(f\) is allowed to grow exponentially is of particular concern and it is shown that global existence without uniform bounds is impossible in one and two dimensions.
- Comenius University
- Comenius University Slovakia
Dirichlet-initial value problems, global existence, large time behaviour, Heat equation, Nonlinear parabolic equations, Initial value problems for second-order parabolic equations, Stability in context of PDEs, blow-up, Analysis
Dirichlet-initial value problems, global existence, large time behaviour, Heat equation, Nonlinear parabolic equations, Initial value problems for second-order parabolic equations, Stability in context of PDEs, blow-up, Analysis
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