Search

Abstract: In this paper, we consider the semilinear wave equation with boundary damping and source terms. This work is devoted to prove a finite time blow-up result under suitable condition on the initial data and positive initial energy. [Copyright &y& Elsevier]

Abstract: In this paper, we consider nonlinear divergence form parabolic equations with inhomogeneous Neumann boundary conditions. We establish respectively the conditions on nonlinearities to guarantee that exists globally or blows up at some finite time. If blow-up occurs, we obtain upper and lower bounds of the blow-up time. [Copyright &y& Elsevier]

Abstract: This paper deals with the blow-up properties of positive solutions to a nonlinear parabolic equation with a localized reaction source and a nonlocal boundary condition. Under certain conditions, the blowup criteria is established. Furthermore, when , , the global blowup behavior is shown, and the blowup rate estimates are also obtained. [Copyright &y& Elsevier]

Abstract: This paper is devoted to a proof of regularity, near the initial state, for solutions to the Cauchy–Dirichlet and obstacle problem for a class of second order differential operators of Kolmogorov type. The approach used here is general enough to allow us to consider smooth obstacles as well as non-smooth obstacles. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with non-simultaneous and simultaneous blow-up for radially symmetric solution to heat equations coupled via nonlinear boundary . It is proved that there exist suitable initial data such that blows up alone if and only if . All of the classifications on the existence of only two components blowing up simultaneously are obtained. We find that different positions (different values of k, i, n) of and leads to quite different blow-up rates. It is interesting that different initial data lead to different blow-up phenomena even with the same requirements on exponent parameters. We also propose that blow up simultaneously while the other ones remain bounded in different exponent regions. Moreover, the blow-up rates and blow-up sets are obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we establish the blow-up rate of the large positive solution of the singular boundary value problem where Ω is a smooth bounded domain in . The weight function is a non-negative continuous function in the domain. is locally Lipschitz continuous and is increasing on and for sufficiently large u with and . Naturally, the blow-up rate of the problem equals its blow-up rate for the very special, but important, case when . We distinguish two cases: (I) Ω is a ball domain and b is a radially symmetric function on the domain in Theorem 1.1; (II) Ω is a smooth bounded domain and b satisfies some local condition on each boundary normal section assumed in Theorem 1.2. The blow-up rate is explicitly determined by functions b and h. In case (I), the singular boundary value problem has a unique solution u satisfying where , and K are defined by In case (II), the blow-up rates of the solutions to the boundary value problem are established and the uniqueness is proved. [Copyright &y& Elsevier]

Abstract: In this paper we study the existence and uniqueness of the global generalized solution and the global classical solution, the blowup of the solution and the energy decay of the solutions of the initial–boundary value problems for a class of nonlinear wave equations. [Copyright &y& Elsevier]

Abstract: For more general nonlinear term g, the paper shows the exact blow-up rate of the unique solution to the singular boundary value problem where , which is positive and non-decreasing on (may vanish at zero). Our results are obtained in a more general setting to those in [S. Cano-Casanova, J. López-Gómez, Existence, uniqueness and blow-up rate of large solutions for a canonical class of one-dimensional problems on the half-line, J. Differential Equations 244 (12) (2008) 3180–3203], where () for sufficiently large u. [Copyright &y& Elsevier]