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Applicable Analysis
An International Journal
Volume 10, 1980 - Issue 2
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Original Articles

On local strong solutions of a nonlinear partial differential equation

Pages 93-104 | Published online: 10 May 2007

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Read on this site (4)

Renato Manfrin. (1998) Global solutions to kirchhoff equations with non-local nonlinearities defined by a potential. Applicable Analysis 69:1-2, pages 1155-1168.
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Gourin Daniel & Mechab Mustapha. (1998) Probleme de cauchy pour des equations de kirchhoff generalisees. Communications in Partial Differential Equations 23:5-6, pages 761-776.
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C.F. Vasconcellos & L.M. Teixeira. (1993) Existence and uniqueness of a solution to a singular thermoelastic contact problem. Applicable Analysis 51:1-4, pages 155-173.
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Eliana Henriques De Brito & Jack Hale. (1982) The damped elastic stretched string equation generalized: existence, uniqueness, regularity and stability. Applicable Analysis 13:3, pages 219-233.
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Articles from other publishers (28)

Ducival PEREİRA & Carlos RAPOSO. (2022) Global Weak Solution, Uniqueness and Exponential Decay for a Class of Degenerate Hyperbolic Equation. Communications in Advanced Mathematical Sciences 5:3, pages 137-149.
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Long Yan & Shuguan Ji. (2016) Global solution and asymptotic behavior for the variable coefficient beam equation with nonlinear damping. Mathematical Methods in the Applied Sciences 39:4, pages 876-885.
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Zai-yun Zhang, Xiu-jin Miao & De ming Yu. (2011) On Solvability and Stabilization of a Class of Hyperbolic Hemivariational Inequalities in Elasticity. Funkcialaj Ekvacioj 54:2, pages 297-314.
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Jemal Peradze. (2009) An Approximate Algorithm for a Kirchhoff Wave Equation. SIAM Journal on Numerical Analysis 47:3, pages 2243-2268.
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Daewook Kim, Keum-Shik Hong & Il Hyo Jung. (2008) Stabilization for the nonlinear beam equation. Stabilization for the nonlinear beam equation.
R. Izaguirre, R. Fuentes & M. Milla Miranda. (2008) Existence of local solutions of the Kirchhoff–Carrier equation in Banach spaces. Nonlinear Analysis: Theory, Methods & Applications 68:11, pages 3565-3580.
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Jemal Peradze. (2005) A numerical algorithm for the nonlinear Kirchhoff string equation. Numerische Mathematik 102:2, pages 311-342.
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Renato Manfrin. (2005) On the global solvability of Kirchhoff equation for non-analytic initial data. Journal of Differential Equations 211:1, pages 38-60.
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Karen Yagdjian. (2003) Geometric optics for the Kirchhoff-type equations. Journal d'Analyse Mathématique 89:1, pages 57-112.
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Karen Yagdjian. (2001) The Lax–Mizohata Theorem for Kirchhoff-Type Equations. Journal of Differential Equations 171:2, pages 346-369.
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Kosuke Ono. (2000) Global existence, asymptotic behaviour, and global non-existence of solutions for damped non-linear wave equations of Kirchhoff type in the whole space. Mathematical Methods in the Applied Sciences 23:6, pages 535-560.
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Mohammed Aassila. (2009) Global existence of solutions to degenerate wave equations with dissipative terms. Bulletin of the Australian Mathematical Society 60:1, pages 1-10.
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M.M Cavalcanti, V.N Domingos Cavalcanti, J.S Prates Filho & J.A Soriano. (1998) Existence and Exponential Decay for a Kirchhoff–Carrier Model with Viscosity. Journal of Mathematical Analysis and Applications 226:1, pages 40-60.
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Tetsu Mizumachi. (1998) Time decay of solutions to degenerate Kirchhoff type equation. Nonlinear Analysis: Theory, Methods & Applications 33:3, pages 235-252.
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Kosuke Ono. (1997) Global Existence, Decay, and Blowup of Solutions for Some Mildly Degenerate Nonlinear Kirchhoff Strings. Journal of Differential Equations 137:2, pages 273-301.
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Solange Kouémou Patcheu. (1997) On a Global Solution and Asymptotic Behaviour for the Generalized Damped Extensible Beam Equation. Journal of Differential Equations 135:2, pages 299-314.
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Kosuke Ono. (1997) On Global Existence, Asymptotic Stability and Blowing Up of Solutions for Some Degenerate Non-linear Wave Equations of Kirchhoff Type with a Strong Dissipation. Mathematical Methods in the Applied Sciences 20:2, pages 151-177.
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Kosuke ONO. (1997) SHARP DECAY ESTIMATES OF SOLUTIONS FOR MILDLY DEGENERATE DISSIPATIVE KIRCHHOFF EQUATIONS. Kyushu Journal of Mathematics 51:2, pages 439-451.
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Piero D'Ancona & Sergio Spagnolo. (2006) Nonlinear perturbations of the kirchhoff equation. Communications on Pure and Applied Mathematics 47:7, pages 1005-1029.
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Helvécio Rubens Crippa. (1993) On local solutions of some mildly degenerate hyperbolic equations. Nonlinear Analysis: Theory, Methods & Applications 21:8, pages 565-574.
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Piero D'Ancona & Sergio Spagnolo. (1993) A class of nonlinear hyperbolic problems with global solutions. Archive for Rational Mechanics and Analysis 124:3, pages 201-219.
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P. D'Ancona & S. Spagnolo. (1992) Global solvability for the degenerate Kirchhoff equation with real analytic data. Inventiones Mathematicae 108:1, pages 247-262.
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Piero D’Ancona & Sergio Spagnolo. 1992. Developments in Partial Differential Equations and Applications to Mathematical Physics. Developments in Partial Differential Equations and Applications to Mathematical Physics 27 32 .
A. Arosio & S. Garavaldi. (1991) On the mildly degenerate Kirchhoff string. Mathematical Methods in the Applied Sciences 14:3, pages 177-195.
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Piero D'Ancona. (1988) Global solution of the cauchy problem for a class of abstract nonlinear hyperbolic equations. Annali di Matematica Pura ed Applicata 151:1, pages 17-38.
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Yoshio Yamada. (1987) Some nonlinear degenerate wave equations. Nonlinear Analysis: Theory, Methods & Applications 11:10, pages 1155-1168.
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Y. Ebihara, L.A. Medeiros & M. Milla Miranda. (1986) Local solutions for a nonlinear degenerate Hyperbolic equation. Nonlinear Analysis: Theory, Methods & Applications 10:1, pages 27-40.
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Kenji Nishihara. (1984) Exponential decay of solutions of some quasilinear hyperbolic equations with linear damping. Nonlinear Analysis: Theory, Methods & Applications 8:6, pages 623-636.
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