## Related Articles

- Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions. Assalé, Louis A.; Boni, Théodore K.; Nabongo, Diabate // Journal of Applied Mathematics;2009, Special section p1
We obtain some conditions under which the positive solution for semidiscretizations of the semilinear equation ut = uxx - a(x,t) f (u), 0 < x < 1, t âˆˆ (0,T), with boundary conditions ux (0,t) = 0, ux (1,t) = b(t) g (u(1,t)), blows up in a finite time and estimate its semidiscrete blow-up...

- QUENCHING OF NUMERICAL SOLUTIONS FOR SOME SEMILINEAR HEAT EQUATIONS WITH A VARIABLE REACTION. N'gohisse, F. K. // Computational Methods in Applied Mathematics;2010, Vol. 10 Issue 1, p95
In this paper, under certain conditions, we show that the solution of the semidiscrete form of a semilinear heat equation with a variable reaction is quenched in a finite time and estimate its semidiscrete quenching time. We also show that the semidiscrete quenching time converges to the...

- ROTHE TIME-DISCRETIZATION METHOD FOR THE SEMILINEAR HEAT EQUATION SUBJECT TO A NONLOCAL BOUNDARY CONDITION. Merazga, Nabil; Bouziani, Abdelfatah // Journal of Applied Mathematics & Stochastic Analysis;Jan2006, p1
This paper is devoted to prove, in a nonclassical function space, the weak solvability of a mixed problem which combines a Neumann condition and an integral boundary condition for the semilinear one-dimensional heat equation. The investigation is made by means of approximation by the Rothe...

- A Remark on the Blowup of Solutions to the Laplace Equations with Nonlinear Dynamical Boundary Conditions. Hongwei Zhang; Qingying Hu // Boundary Value Problems;2010, Special section p1
We present some sufficient conditions of blowup of the solutions to Laplace equations with semilinear dynamical boundary conditions of hyperbolic type.

- A NOTE ON GLOBAL WELL-POSEDNESS AND BLOW-UP OF SOME SEMILINEAR EVOLUTION EQUATIONS. SAANOUNI, TAREK // Evolution Equations & Control Theory;Sep2015, Vol. 4 Issue 3, p355
We investigate the initial value problems for some semilinear wave, heat and SchrÃ¶Ã¶dinger equations in two space dimensions, with exponential nonlinearities. Using the potential well method based on the concepts of invariant sets, we prove either global well-posedness or finite time blow-up.

- On growth rate near the blowup surface for semilinear wave equations. Merle, Frank; Zaag, Hatem // IMRN: International Mathematics Research Notices;2005, Vol. 2005 Issue 19, p1127
We find the optimal growth estimate near the blowup surface for the semilinear wave equation with a power nonlinearity. The techniques are based on local energy estimates of our earlier work, which extend to the present situation. The exponent p is superlinear and less than or equal to...

- Transversality of stable and Nehari manifolds for a semilinear heat equation. Dickstein, Flavio; Mizoguchi, Noriko; Souplet, Philippe; Weissler, Fred // Calculus of Variations & Partial Differential Equations;Nov2011, Vol. 42 Issue 3/4, p547
It is well known that for the subcritical semilinear heat equation, negative initial energy is a sufficient condition for finite time blowup of the solution. We show that this is no longer true when the energy functional is replaced with the Nehari functional, thus answering negatively a...

- A Numerical Investigation of Blow-up in The Moving Heat Source Problems in Two-dimensions. Hancan Zhu; Kewei Liang // WSEAS Transactions on Mathematics;Mar2013, Vol. 12 Issue 3, p286
The temperature of a combustible material will rise or even blow up when a heat source moves across it. In this paper, we study the blow-up phenomenon in this kind of moving heat source problems in two-dimensions. First, a two-dimensional heat equation with a nonlinear source term is introduced...

- Remarks on the Semilinear Wave Equations. Abu Naim Sheikh, Md. // Vietnam Journal of Mathematics;Mar2000, Vol. 28 Issue 1, p17
Focuses on the semilinear wave equation. Condition on the local existence of the equation; Local existence theorem of the equation; Reaction of the local solution in finite time for negative initial energy.

- SOLUTION TO A SEMILINEAR PSEUDOPARABOLIC PROBLEM WITH INTEGRAL CONDITIONS. Bouziani, Abdelfatah; Merazga, Nabil // Electronic Journal of Differential Equations;2006, Vol. 2006, Special section p1
In this article, we use the Rothe time-discretization method to prove the well-posedness of a mixed problem with integral conditions for a third order semilinear pseudoparabolic equation. Also we establish the convergence of the method and an error estimate for a semi-discrete approximation.