On global regular solutions of third order partial differential equations

DOI10.1016/0022-247X(80)90033-5zbMath0429.35057MaRDI QIDQ1137726

Hartmut Pecher

Publication date: 1980

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Sobolev spaceCauchy problemnonlinearitiesanalytic semigroupsenergy inequalityunique global smooth solutiona- priori estimatesthird order partial differential equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) A priori estimates in context of PDEs (35B45) Partial differential equations of mathematical physics and other areas of application (35Q99) General first-order partial differential equations and systems of first-order partial differential equations (35F99)

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Cites Work

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• On the existence, uniqueness, and stability of solutions of the equation \(p_0 {\mathfrak X}_{tt} = E({\mathfrak X}_ x) {\mathfrak X}_{xx} +\lambda {\mathfrak X}_{xxt}\)
• On the Existence and Uniqueness of Solutions of the Equation
• On global solutions for mixed problem of a semi-linear differential equation