The Blow-Up Profile for a Fast Diffusion Equation with a Nonlinear Boundary Condition

Ferreira, Raúl; Pablo, Arturo de; Quirós, Fernando; Rossi, Julio D.

doi:10.1216/rmjm/1181069989

Cited by 30 publications

(38 citation statements)

References 22 publications

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“…The picture depends obviously on p, but also crucially on the initial data. In fact, there always exist global solutions for every p > 0, contrary to what occurs for problem (1.2) with r < 1, where every solution blows up if (2 − r)/2 < p ≤ 2 − r independently of the initial condition, see [8,14]. In the sequel we assume that u 0 has compact support [0, N ].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…Problem (1.1) can be viewed as a limit case for the family of problems The blow-up phenomenon for this problems has been extensively studied in the works [8,11,12,14,17,22], both for the half-line or a bounded interval. If on the contrary r > 1, we obtain m < 0, q < 0 and c < 0.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…This kind of transformation goes back to [2,19], and is used for instance in [8,18]. The resulting system is (2.6)…”

Section: In Particular U Is Lipschitz Continuous In Spacementioning

confidence: 99%

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Blow-up for a degenerate diffusion problem not in divergence form

Pablo¹,

Ferreira²,

Rossi³

2006

Indiana Univ. Math. J.

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Abstract. We study the behaviour of solutions of the nonlinear diffusion equation in the half-line, R + = (0, ∞), with a nonlinear boundary condition,with p > 0. We describe in terms of p and the initial datum when the solution is global in time and when it blows-up in finite time. For blowing up solutions we find the blow-up rate and the blow-up set and we describe the asymptotic behaviour close to the blow-up time in terms of a self-similar profile. The stationary character of the support is proved both for global solutions and blowing-up solutions. Also we obtain results for the problem in a bounded interval.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Blow-up for a degenerate diffusion problem not in divergence form

Pablo¹,

Ferreira²,

Rossi³

2006

Indiana Univ. Math. J.

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“…In the wake of the pioneering work of Fujita [4], many results on critical Fujita exponents for diffusion equations with nonlinear sources can be found; see [1][2][3][4][5][7][8][9]. It was Ferreira et al [3] who considered the fast diffusive equation with nonlinear boundary sources:…”

Section: Introductionmentioning

confidence: 99%

“…It was Ferreira et al [3] who considered the fast diffusive equation with nonlinear boundary sources:…”

Section: Introductionmentioning

confidence: 99%

Critical Curves for a Coupled System of Fast Diffusive Newtonian Filtration Equations

Wang²

2012

Bull. Aust. Math. Soc.

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This paper deals with the large-time behaviour of solutions to the fast diffusive Newtonian filtration equations coupled via the nonlinear boundary sources. A result of Fujita type is obtained by constructing various kinds of upper and lower solutions. In particular, it is shown that the critical global existence curve and the critical Fujita curve concide for the multi-dimensional system. This is quite different from the known results obtained in Wang, Zhou and Lou ['Critical exponents for porous medium systems coupled via nonlinear boundary flux', Nonlinear Anal.

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Critical exponent for non‐Newtonian filtration equation with homogeneous Neumann boundary data

Wang

Yin

Lusheng

2007

Math Methods in App Sciences

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SUMMARYThis paper is concerned with large time behavior of solutions to the homogeneous Neumann problem of the non-Newtonian filtration equation. It is shown that the critical Fujita exponent for the problem considered is determined not only by the spatial dimension and the nonlinearity exponent, but also by the coefficient k of the first-order term. In fact, we show that there exist two thresholds k ∞ and k 1 on the coefficient k of the first-order term, and the critical Fujita exponent is a finite number when k is between k ∞ and k 1 , while the critical exponent does not exist when k k ∞ or k k 1 .

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The Blow-Up Profile for a Fast Diffusion Equation with a Nonlinear Boundary Condition

Cited by 30 publications

References 22 publications

Blow-up for a degenerate diffusion problem not in divergence form

Blow-up for a degenerate diffusion problem not in divergence form

Critical Curves for a Coupled System of Fast Diffusive Newtonian Filtration Equations

Critical exponent for non‐Newtonian filtration equation with homogeneous Neumann boundary data

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