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César Adolfo Melo Hernández Edgar Yesid Lancheros Mayorga 《Mathematische Nachrichten》2020,293(4):721-734
In this paper, information about the instability of equilibrium solutions of a nonlinear family of localized reaction-diffusion equations in dimension one is provided. More precisely, explicit formulas to the equilibrium solutions are computed and, via analytic perturbation theory, the exact number of positive eigenvalues of the linear operator associated to the stability problem is analyzed. In addition, sufficient conditions for blow up of the solutions of the equation are also discussed. 相似文献
84.
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This paper deals with the initial boundary value problem for strongly damped semilinear wave equations with logarithmic nonlinearity in a bounded domain . We discuss the existence, uniqueness and polynomial or exponential energy decay estimates of global weak solutions under some appropriate conditions. Moreover, we derive the finite time blow up results of weak solutions, and give the lower and upper bounds for blow-up time by the combination of the concavity method, perturbation energy method and differential–integral inequality technique. 相似文献
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88.
Hayato Nawa 《Journal of statistical physics》1998,91(1-2):439-458
We consider the blow-up problem for the nonlinear Schrödinger equation with quartic self-interacting potential on
. We exhibit a class of initial data leading to the blow-up solutions which have at least two L
2-concentration points. 相似文献
89.
L.E. Payne 《Journal of Mathematical Analysis and Applications》2008,338(1):438-447
A first order differential inequality technique is used on suitably defined auxiliary functions to determine lower bounds for blow-up time in initial-boundary value problems for parabolic equations of the form
ut=div(ρ(u)gradu)+f(u) 相似文献
90.
刘慈群 《应用数学和力学(英文版)》1988,9(6):521-252
The transient spherical flow behavior of a slightly compressible non-Newtonian, power-law fluids in porous media is studied.
A nonlinear partial differential equation of parabolic type is derived. The diffusivity equation for spherical flow is a special
case of the new equation. We obtain analytical, asymptotic and approximate solutions by using the methods of Laplace transform
and weighted mass conservation. The structures of asymptotic and approximate solutions are similar, which enriches the theory
of one-dimensional flow of non-Newtonian fluids through porous media. 相似文献