Results 251 to 260 of about 13,013,114 (294)

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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