… Motivated by a recent work of Galaktionov [4] on blow-up problems, we shall describe the
quenching behavior of the solution near the quenching point by constructing a Lyapunov …

… the behavior of (A) beyond quenching. Their results are also incomplete in this regard. The
lack of uniqueness makes it difficult to study the problem beyond quenching. … and quenching …

… near the quenching point. … the quenching behavior: the measure of the vanishing set { ( t ,
x ) ∈ [ 0 , + ∞ ) × Ω : u ( t , x ) = 0 } is positive. It is also shown that the possibility of quenching in …

… parabolic equation with a moving nonlinear source. The study presents criteria for both
finite-time quenching … to v ∗ , while finite-time quenching occurs when the speed is smaller than v …

… -electromechanical system (MEMS for short) device model. In this paper, the author first gives
an asymptotic behavior of the quenching time T* for the solution u to the parabolic problem …

… -time quenching for the nonlinear parabolic system with coupled … quenching of solutions,
and then determine the blow-up of time-derivatives and the quenching set for the quenching …

… the blow-up and quench ing phenomena for solutions of some parabolic equations. In Chapter
… that the quenching case is not so amenable to analysis. Therefore, we conduct numerical …

… uniformly parabolic. Therefore, in order to study the behavior of u near the quenching time,
we … by a singular two-dimensional dynamical system, and this implies a delicate mathematical …

This study is concerned with a family of parabolic system with general singular nonlinearities,
which is a generalization of MEMS system. To some extent, the classification of global …

… In this paper, we study the quenching phenomena for a one-dimensional parabolic system
… On the quenching behavior of the solution of a semilinear parabolic equations. J. Math. …