Monotone solutions to quasilinear parabolic equations
Copyright policy )Monotone solutions to quasilinear parabolic equations
General quasilinear parabolic equations on a bounded domain in \(\mathbb{R}^ N\) under linear boundary conditions are considered. Due to the maximum principle, the solution flows of such equations belong to the class of strongly monotone (order preserving) dynamical systems. The main result of the present contribution states that if the nonlinearities in the equation are real analytic and some growth and dissipative conditions are satisfied then most solutions (that is, solutions emanating from an open and dense set of initial conditions) become eventually monotone in time.
analytic nonlinearities, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Initial-boundary value problems for second-order parabolic equations, monotonicity in time, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, quasilinear parabolic equations, strongly monotone dynamical systems
analytic nonlinearities, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Initial-boundary value problems for second-order parabolic equations, monotonicity in time, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, quasilinear parabolic equations, strongly monotone dynamical systems
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