The Cauchy problem for a second-order nonlinear hyperbolic equation with initial data on a line of parabolicity

DOI10.1017/S0004972700011060zbMath0415.35054MaRDI QIDQ3050855

John Michael S. Rassias

Publication date: 1979

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

iterationsingular integral equationsCauchy problemunique regular solutionnon-linear hyperbolic equationinitial data on a line of parabolicity

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order nonlinear hyperbolic equations (35L70) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)

Cites Work

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• A nonlinear singular Cauchy problem
• A uniqueness theorem for a singular Cauchy problem
• On the unique solution of the singular Cauchy problem for a quasi-linear equation
• A quasi-linear singular Cauchy problem
• A singular Cauchy problem
• Sul problema di Cauchy per l'equazione \(y^{2\alpha}k^2 (x,y)z_{xx}-z_{yy} =f(x,y,z,z_x,z_y)\) con i dati sulla linea parabolica
• On nonlinear partial differential equations with two independent variables
• The Cauchy Problem for a Hyperbolic Second Order Equation with Data on the Parabolic Line

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