Complicated dynamics of parabolic equations with simple gradient dependence

DOI10.1090/S0002-9947-98-02294-6zbMath0897.35040MaRDI QIDQ4211094

Martino Prizzi, Krzysztof P. Rybakowski

Publication date: 10 September 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

chaosreaction-diffusion-convection equationscenter manifoldsjet realizationlinear dependence on \(\nabla u\)

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (5)

Schoenflies spheres as boundaries of bounded unstable manifolds in gradient Sturm systems ⋮ Unnamed Item ⋮ Inverse problems and chaotic dynamics of parabolic equations on arbitrary spatial domains ⋮ Some generic properties of Schrödinger operators with radial potentials ⋮ A remark on the existence of suitable vector fields related to the dynamics of scalar semi-linear parabolic equations

Cites Work

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• Imbedding of any Vector Field in a Scalar Semilinear Parabolic Equation
• Realization of vector fields and dynamics of spatially homogeneous parabolic equations
• Realisation of ordinary differential equations by retarded functional differential equations in neighbourhoods of equilibrium points

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