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Uniform blow-up rate for compressible reactive gas model
Applied Mathematics and Mechanics, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xu, Run-zhang, Jiang, Xiao-li, Liu, Jie
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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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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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Boundary blow‐up rate of solutions to elliptic cooperative systems
Mathematical Methods in the Applied Sciences, 2019AbstractThis paper shows the existence, uniqueness, and boundary blow‐up rate of large solution of cooperative systems of the form in a bounded smooth domain Ω⊂RN, bi(x) is nonnegative weight function that can be singular on ∂Ω, and the exponents verify λi∈R,ai>0,pi>1,qi>0 for i=1,2, and q1q2<p1p2.
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On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
Mathematische Zeitschrift, 2000In 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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Applied Mathematics and Computation, 2014
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Zhu, Shihui, Yang, Han, Zhang, Jian
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Zhu, Shihui, Yang, Han, Zhang, Jian
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Uniform blow-up rate for a nonlocal degenerate parabolic equations
Nonlinear Analysis: Theory, Methods & Applications, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Qilin, Li, Yuxiang, Gao, Hongjun
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Blow up rate for semilinear heat equations with subcritical nonlinearity
Indiana University Mathematics Journal, 2004The blow up rate of sign-changing solutions of the Cauchy problem for a semilinear heat equation is established under the assumption that the nonlinear source term is a subcritical power. This was known before for positive solutions, but for sign-changing solutions only a partial result was available [see \textit{Y. Giga} and \textit{R. V.
Giga, Y., Matsui, S., Sasayama, S.
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Decay rate and blow up solutions for coupled quasilinear system
Boletín de la Sociedad Matemática Mexicana, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nadia Mezouar, Erhan PİŞKİN
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Blow-up rates of large solutions for infinity Laplace equations
Applied Mathematics and Computation, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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