• Honam Mathematical Journal
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• v.43 no.4
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• pp.667-678
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• 2021

Blow-up phenomena for a nonlocal reaction-diffusion system with time-dependent coefficients are investigated under null Dirichlet boundary conditions. Using Kaplan's method with the comparison principle, we establish new blow-up criteria and obtain the upper bounds for the blow-up time of the solution under suitable measure sense in the whole-dimensional space.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1143-1158
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• 2020

In this paper, we are concerned with the blow-up phenomena for a class of pseudo-parabolic equations with weighted source u_t - △u - △u_t = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions in any smooth bounded domain Ω ⊂ ℝⁿ (n ≥ 1). Firstly, we obtain the upper and lower bounds for blow-up time of solutions to these problems. Moreover, we also give the estimates of blow-up rate of solutions under some suitable conditions. Finally, three models are presented to illustrate our main results. In some special cases, we can even get some exact values of blow-up time and blow-up rate.

• Kyungpook Mathematical Journal
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• v.61 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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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 Mathematical Society
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• v.56 no.4
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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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.4
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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.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.425-430
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• 2010

In this work, We consider an initial boundary value problem for a class of nonlinear hyperbolic equations. We establish a blow-up result for certain solutions with a dissipative term.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.633-642
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• 2021

In this paper we consider the following strongly damped wave equation with variable-exponent nonlinearity u_tt(x, t) - ∆u(x, t) - ∆u_t(x, t) = |u(x, t)|^p(x)-2u(x, t), where the exponent p(·) of nonlinearity is a given measurable function. We establish finite time blow-up results for the solutions with non-positive initial energy and for certain solutions with positive initial energy. We extend the previous results for strongly damped wave equations with constant exponent nonlinearity to the equations with variable-exponent nonlinearity.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.3
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• pp.287-308
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• 2018

This paper deals with blow-up phenomena for an initial boundary value problem of a quasilinear parabolic equation with time-dependent coefficient in a bounded star-shaped region under nonlinear boundary flux. Using the auxiliary function method and differential inequality technique, we establish some conditions on time-dependent coefficient and nonlinear functions for which the solution u(x, t) exists globally or blows up at some finite time $t^*$. Moreover, some upper and lower bounds for $t^*$ are derived in higher dimensional spaces. Some examples are presented to illustrate applications of our results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.4
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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.