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Blow-up in complex time

, 2017
Stuke, Hannes
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Blow-up and blow-up rate for a reaction–diffusion model with multiple nonlinearities

Nonlinear Analysis: Theory, Methods & Applications, 2003
Let \(\Omega\subset\mathbb R^n\) be a smoothly bounded domain, \(m,\alpha,\beta>0\). Condider the equation \((u^m)_t=\Delta u+u^\alpha\) in \(\Omega\times(0,T)\), complemented by the nonlinear boundary condition \(\partial u/\partial\nu=u^\beta\) and the initial condition \(u(x,0)=u_0(x)\), where \(u_0\) is a positive function satisfying the ...
Song, Xianfa, Zheng, Sining
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Non-simultaneous blow-up and blow-up rates for reaction–diffusion equations

Nonlinear Analysis: Real World Applications, 2012
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Liu, Bingchen, Li, Fengjie
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On the blow-up rate and the blow-up set of breaking waves for a shallow water equation

Mathematische Zeitschrift, 2000
In a previous paper [Commun. Pure Appl. Math. 51, No. 5, 475-504 (1998; Zbl 0934.35153)], the authors proved the well-posedness of the Cauchy problem for the periodic Camassa-Holm equation with initial data \(u_0\) belonging to the Sobolev space \(H^3(\mathbb{S})\), \(\mathbb{S}\) the unit circle. Sufficient blow-up conditions where also given.
Constantin, Adrian, Escher, Joachim
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Existence and boundary blow-up rates of solutions for boundary blow-up elliptic systems

Nonlinear Analysis: Theory, Methods & Applications, 2009
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Wang, Mingxin, Wei, Lei
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Blow-up, blow-up rate and decay of the solution of the weakly dissipative Camassa-Holm equation

Journal of Mathematical Physics, 2006
In this paper, we mainly study several problems on the weakly dissipative periodic Camassa-Holm equation. At first, the local well-posedness of the equation is obtained by Kato’s theorem, a necessary and sufficient condition of the blow-up of the solution and some criteria guaranteeing the blow-up of the solution are established. Then, the blow-up rate
Wu, Shuyin, Yin, Zhaoyang
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Blow-up rate, mass concentration and asymptotic profile of blow-up solutions for the nonlinear inhomogeneous Schrödinger equation

Applied Mathematics and Computation, 2014
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Shihui Zhu, Han Yang, Jian Zhang 0065
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Finite-time blow-up and blow-up rates for the Gierer–Meinhardt system

Applicable Analysis, 2014
In this paper, we consider the Gierer–Meinhardt system (1.1), shown below, on a bounded smooth domain () with a homogeneous Neumann boundary condition. Under suitable conditions on the exponents , , , and , we establish sufficient conditions for finite-time blow-up and obtain blow-up rates for blow-up solutions.
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Blow-Up Rate

2011
It is established in Chap. 5 that the nonlinearity causes the blow-up to occur at a finite time in certain situations. If the solution to the ODE \(u_t \,= \,f(u)\), blows up at a finite time t = T with \(u(T - 0) = +\infty\), then u = G(T - t), where \(G(\xi)\) is the inverse function of \(\int\nolimits_\infty^u \frac {dn}{f(n)}\)
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Blow-up rates for parabolic systems

ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1996
Two weakly coupled systems of parabolic equations are considered. One is coupled in the equations and the other in the boundary conditions. For both of them blow-up in finite time may occur. Estimates of the blow-up rates (in \(t\)) are established for certain classes of initial functions.
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