Phragmén-Lindelôf Type Theorems for Some Semilinear Elliptic and Parabolic Equations

Çelebi, A. Okay; Kalantarov, Varga K.; Tahamtani, Faramarz

doi:10.1515/dema-1998-0107

Cited by 3 publications

(3 citation statements)

References 8 publications

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“…Thus, it is worth recalling some recent contributions concerning the spatial behavior of solutions of nonlinear parabolic equations and/or nonlinear boundary conditions [4,5,9,13,15,17,18]. Here, we give sufficient conditions on the data of the problem to guarantee either the spatial decay or the spatial blow-up of solutions.…”

Section: Introductionmentioning

confidence: 99%

On the spatial blow-up and decay for some nonlinear parabolic equations with nonlinear boundary conditions

Quintanilla

2006

Z. angew. Math. Phys.

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In this note we investigate the spatial behavior of several nonlinear parabolic equations with nonlinear boundary conditions. Under suitable conditions on the nonlinear terms we prove that the solutions either cease to exist for a finite value of the spatial variable or else they decay algebraically. The main tool used is the weighted energy method. Our results can be applied to several situations concerning heat conduction.

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Section: Introductionmentioning

confidence: 99%

On the spatial blow-up and decay for some nonlinear parabolic equations with nonlinear boundary conditions

Quintanilla

2006

Z. angew. Math. Phys.

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“…The history and development of this question is explained in the work of Horgan and Knowles [1]. The interested reader is referred to the papers [2][3][4][5][6][7][8][9] and the reviews by Horgan and Knowles [1,10,11]. The energy method is widely used to study such results.…”

Section: Introductionmentioning

confidence: 99%

Spatial estimates for a class of hyperbolic equations with nonlinear dissipative boundary conditions

Tahamtani

2011

Bound Value Probl

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“…Alternatively, the results may be viewed as theorems of Phragmén-Lindelöf type [1,8,14] for nonlinear damped hyperbolic equations.…”

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confidence: 99%

Spatial decay estimates for a class of nonlinear damped hyperbolic equations

Tahamtani

Mosaleheh

Seddighi

2001

International Journal of Mathematics and Mathematical Sciences

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Abstract. This paper is concerned with investigating the spatial decay estimates for a class of nonlinear damped hyperbolic equations. In addition, we compare the solutions of two-dimensional wave equations with different damped coefficients and establish an explicit inequality which displays continuous dependence on this coefficient.2000 Mathematics Subject Classification. 35B45, 35L70, 80A20, 30C80.

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Phragmén-Lindelôf Type Theorems for Some Semilinear Elliptic and Parabolic Equations

Abstract: Abstract. Phragmén-Lindelöf type theorems for some classes of fourth order semilinear elliptic and second order quasi-linear parabolic equations are proved.

Cited by 3 publications

References 8 publications

On the spatial blow-up and decay for some nonlinear parabolic equations with nonlinear boundary conditions

On the spatial blow-up and decay for some nonlinear parabolic equations with nonlinear boundary conditions

Spatial estimates for a class of hyperbolic equations with nonlinear dissipative boundary conditions

Spatial decay estimates for a class of nonlinear damped hyperbolic equations

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