The beam equation with nonlinear memory

DOI10.1007/s00033-016-0655-xzbMath1361.35116OpenAlexW2346157951MaRDI QIDQ322127

Sandra Lucente, Marcello D'Abbicco

Publication date: 14 October 2016

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-016-0655-x

zbMATH Keywords

local-in-time solutionsnonhomogeneous Sobolev spacessmall data global solutions

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Critical exponents in context of PDEs (35B33) Initial value problems for higher-order hyperbolic equations (35L30) Higher-order semilinear hyperbolic equations (35L76)

Related Items (6)

Large data solutions for semilinear higher order equations ⋮ A new phenomenon in the critical exponent for structurally damped semi-linear evolution equations ⋮ Blow-up result for a semilinear wave equation with a nonlinear memory term ⋮ Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term. ⋮ Global well-posedness for effectively damped wave models with nonlinear memory ⋮ A note on optimal L 2 -estimates of solutions to some strongly damped σ-evolution equations

Cites Work

• Strichartz estimates for the vibrating plate equation
• Nonlinear Liouville theorems for Grushin and Tricomi operators.
• Existence of solitons in the nonlinear beam equation
• A wave equation with structural damping and nonlinear memory
• Racine carrée d'une fonction différentiable
• Scattering and the Levandosky-Strauss conjecture for fourth-order nonlinear wave equations
• An equation whose Fujita critical exponent is not given by scaling
• A note on the lifespan of solutions to the semilinear damped wave equation
• A modified test function method for damped waves
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