Countable branching of similarity solutions of higher-order porous medium type equations
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Publication:1028499
zbMath1182.35070MaRDI QIDQ1028499
Publication date: 30 June 2009
Published in: Advances in Differential Equations (Search for Journal in Brave)
self-similar solutionsbranchingcountable set of solutionsfourth-order porous medium equationhigher-order porous medium equationsixth-order porous medium equation
Degenerate parabolic equations (35K65) Bifurcations in context of PDEs (35B32) Initial value problems for higher-order parabolic equations (35K30) Semilinear parabolic equations (35K58) Self-similar solutions to PDEs (35C06)
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The Cauchy problem for a tenth-order thin film equation. I. bifurcation of oscillatory fundamental solutions ⋮ Weak solutions for a sixth-order thin film equation ⋮ The Cauchy problem for a tenth-order thin film equation. II: Oscillatory source-type and fundamental similarity solutions ⋮ Eigenfunctions and Very Singular Similarity Solutions of Odd‐Order Nonlinear Dispersion PDEs: Toward a “Nonlinear Airy Function” and Others ⋮ On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation. I: Local oscillatory properties
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