• 대한수학회지
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• 제56권4호
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• pp.1017-1029
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• 2019

In this paper, blows-up and global solutions for a class of nonlinear divergence form parabolic equations with the abstract form of $({\varrho}(u))_t$ and time dependent coefficients are considered. The conditions are established for the existence of a solution globally and also the conditions are established for the blow up of the solution at some finite time. Moreover, the lower bound and upper bound of the blow-up time are derived if blow-up occurs.

• 대한수학회보
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• 제56권5호
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• pp.1285-1296
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• 2019

This paper deals with the blow-up phenomenon of solutions to a pseudo-parabolic equation with logarithmic nonlinearity, which was studied extensively in recent years. The previous result depends on the mountain-pass level d (see (1.6) for its definition). In this paper, we obtain two blow-up conditions which do not depend on d. Moreover, the upper bound of the blow-up time is obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권4호
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• pp.235-242
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• 2012

In this paper, we investigate a nonlocal semilinear heat equation with homogeneous Dirichlet boundary condition in a bounded domain, and prove that there exist solutions with positive initial energy that blow up in finite time.

• 충청수학회지
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• 제35권2호
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• pp.137-147
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• 2022

In this paper, we considered the Dirichlet initial boundary value problem of a nonlinear viscoelastic wave equation with nonlinear damping and source terms, and investigated finite time blow-up phenomena of the solutions to the equation with arbitrary positive initial data, under suitable conditions.

• 대한수학회보
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• 제51권6호
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• pp.1697-1710
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• 2014

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Meanwhile, under the condition of the positive initial energy, it is showed that the solutions blow up in the finite time and the lifespan estimate of solutions is also given.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.547-554
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• 2014

In this paper, we consider the existence and uniqueness of global weak solution for a sixth-order classical surface-diffusion equation in one spatial dimension. Moreover, the regularity and blow-up of solutions are also studied.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권4호
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• pp.243-248
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• 2012

We consider the (possible) finite time blow-up of the smooth solutions of the 3D incompressible Euler equations in a smooth domain or in $R^3$. We derive blow-up criteria in terms of $L^{\infty}$ of the partial component of Hessian of the pressure together with partial component of the vorticity.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.1-10
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• 2021

This paper is concerned the finite time blow-up of solution for higher-order nonlinear Kirchhoff-type equation with a degenerate term and a source term. By an appropriate Lyapunov inequality, we prove the finite time blow-up of solution for equation (1.1) as a suitable conditions and the initial data satisfying ||Dmu0|| > B-(p+2)/(p-2q), E(0) < E1.

• 충청수학회지
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• 제23권4호
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• pp.773-784
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• 2010

The existence of solutions in Besov spaces for nonlinear heat equations having transcendental nonlinearity: $$\frac{\partial}{{\partial}t}u-{\Delta}u=F(u)$$ is investigated. In particular, it is proved the local existence and blow-up phenomena of the solutions in Besov spaces for nonlinear heat equations corresponding to two transcendental nonlinear functions $F(u){\equiv}{\mid}u{\mid}e^{u^2}$ and $F(u){\equiv}e^u$ of rapid growth.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.631-649
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• 2019

In this paper, we prove the global nonexistence of solutions for a quasilinear wave equation with time delay and acoustic boundary conditions. Further, we establish the blow up result under suitable conditions.