Conditions For Blow-up Of Solutions Research Articles

Blow-Up of Solutions to Fractional-in-Space Burgers-Type Equations

We consider fractional-in-space analogues of Burgers equation and Korteweg-de Vries-Burgers equation on bounded domains. Namely, we establish sufficient conditions for finite-time blow-up of solutions to the mentioned equations. The obtained conditions depend on the initial value and the boundary conditions. Some examples are provided to illustrate our obtained results. In the proofs of our main results, we make use of the test function method and some integral inequalities.

Wave-breaking phenomena and global existence for the generalized Fornberg-Whitham equation

We consider the initial value problem for the generalized Fornberg-Whitham equation, which consists of p-order nonlinear advection term and nonlocal dispersion term. In the case of p=2, we study sufficient conditions for blow-up of solutions and some relations to the Burgers equation. Also, for p≥5, we show the global existence of the solutions with small initial data.

Blow-up of solutions of strongly dissipative generalized Klein–Gordon equations

We study the question of sufficient conditions for blow-up of solutions of a model initial-boundary value problem. We use a modified form of Levine's method to obtain sufficient conditions for blow-up in finite time.

Sharp conditions for blowup of solutions of a chemotactical model for two species in [formula omitted

We consider a model system of Keller–Segel type for the evolution of two species in the whole space R2 which are driven by chemotaxis and diffusion. It is well known that this problem admits global and blowup solutions. We show that there exists a sharp condition which allows to distinguish global and blowup solutions in the radially symmetric case. More precisely, let m∞ and n∞ be the total masses of the species. Then there exists a critical curve γ in the m∞−n∞ plane such that the solution blows up if and only if (m∞,n∞) is above γ. This gives an answer to a question raised by Conca et al. (2011) in [8]. We also study the asymptotic behaviour of global solutions in the subcritical case, showing that they are asymptotically self-similar.

On the absence of local solutions of several evolutionary problems

We consider the existence problem for local (with respect to time) solutions of quasilinear evolutionary partial differential equations and inequalities with singular coefficients and initial conditions. We obtain sufficient conditions for instantaneous blow-up of solutions and show that the results thus obtained cannot be improved in the function class under study.

Blow-up conditions for nonlinear Volterra integral equations with power nonlinearity

In this work we consider nonlinear Volterra equations of a special type. We find necessary and sufficient conditions for blow-up of solutions to this class of equations.

Conditions for blow-up of solutions of some nonlinear Volterra integral equations

In this paper we give necessary and sufficient conditions for blow-up of solutions for a particular class of nonlinear Volterra equations. We also give some examples.

Complete blow-up for quasilinear degenerate parabolic equations

Non-negative post-blow-up solutions of the quasilinear degenerate parabolic equation in RN (or a bounded domain with Dirichlet boundary condition) are studied. Various sufficient conditions for complete blow-up of solutions are given.