Results 21 to 30 of about 396,174 (280)
Stability of Blow-Up Profile and Lower Bounds for Blow-Up Rate for the Critical Generalized KdV Equation [PDF]
The Annals of Mathematics, 2002 The generalized Korteweg-de Vries equations are a class of Hamiltonian systems in infinite dimension derived from the KdV equation where the quadratic term is replaced by a higher order power term. These equations have two conservation laws in the energy space H^1(L^2 norm and energy).
Martel, Yvan, Merle, Frank
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Blow-up results of the positive solution for a class of degenerate parabolic equations
Open Mathematics, 2021 This paper is devoted to discussing the blow-up problem of the positive solution of the following degenerate parabolic equations: (r(u))t=div(∣∇u∣p∇u)+f(x,t,u,∣∇u∣2),(x,t)∈D×(0,T∗),∂u∂ν+σu=0,(x,t)∈∂D×(0,T∗),u(x,0)=u0(x),x∈D¯.\left\{\begin{array}{ll}{(r ...
Dong Chenyu, Ding Juntang
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On explosive solutions for a class of quasi-linear elliptic equations [PDF]
, 2012 We study existence, uniqueness, multiplicity and symmetry of large solutions for a class of quasi-linear elliptic equations. Furthermore, we characterize the boundary blow-up rate of solutions, including the case where the contribution of boundary ...
Gladiali, Francesca, Squassina, Marco
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Differential Equations and Nonlinear Mechanics, 2007 This paper investigates the local existence of the nonnegative solution and the finite time blow-up of solutions and boundary layer profiles of diffusion equations with nonlocal reaction sources; we also study the global existence and that the rate of ...
Zhoujin Cui, Zuodong Yang
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Blow-Up Rate Estimates for a System of Reaction-Diffusion Equations with Gradient Terms
International Journal of Mathematics and Mathematical Sciences, 2019 This paper is concerned with the blow-up properties of Cauchy and Dirichlet problems of a coupled system of Reaction-Diffusion equations with gradient terms. The main goal is to study the influence of the gradient terms on the blow-up profile.
Maan A. Rasheed +2 more
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Serre-Green-Naghdi Dynamics under the Action of the Jeffreys’ Wind-Wave Interaction
Fluids, 2022 We derive the anti dissipative Serre-Green-Naghdi (SGN) equations in the context of nonlinear dynamics of surface water waves under wind forcing, in finite depth.
Miguel Alberto Manna, Anouchah Latifi
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On the blow-up rate for fast blow-up solutions arising in an anisotropic crystalline motion
Journal of Computational and Applied Mathematics, 2003 The authors study an anisotropic motion of closed, convex polygonal curves by a power of crystalline curvature in the plane. They mainly discuss the degenerate pinching singularity and show the exact blow-up rate for a fast blow-up solution which arises in an equivalent blow-up problem.
Ishiwata, Tetsuya, Yazaki, Shigetoshi
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Rate of decay for the mass ratio of pseudo-holomorphic integral 2-cycles [PDF]
, 2015 We consider any pseudo holomorphic integral 2-cycle in an arbitrary almost complex manifold and perform a blow up analysis at an arbitrary point. Building upon a pseudo algebraic blow up (previously introduced by the author) we prove a geometric rate of ...
Bellettini, Costante
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Abstract and Applied Analysis, 2014 We study the blow-up and global solutions for a class of quasilinear parabolic problems with Robin boundary conditions. By constructing auxiliary functions and using maximum principles, the sufficient conditions for the existence of blow-up solution, an ...
Juntang Ding
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The Blow-Up Rate for a Semilinear Parabolic System
Journal of Mathematical Analysis and Applications, 1999 This paper considers the blow-up of solutions of the semilinear parabolic system \[ {\partial u_i\over\partial t}=\Delta u_i+ u^{p_i}_{i+1},\quad i=1,2,\dots, k,\quad u_{k+1}: =u_1,\quad x\in\mathbb{R}^N,\;0{1\over 2}N\), then any solution which blows up in time \(T\) satisfies \(u_i(x,t)\leq C(T-t)^{\alpha_i}\), \(i=1,2, \dots,k\), \((x,t)\in\mathbb{R}
Fila, Marek, Quittner, Pavol
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