Periodic solutions of systems of parabolic equations in unbounded domains

In this paper we show that the second-order differential solution is 𝕃2-almost periodic, provided it is 𝕃2-bounded, and the growth of the components of a non-linear function of a system of parabolic equation is bounded by any pair of con-secutive eigenvalues of the associated Dirichlet boundary value problems.

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Unstable periodic wave solutions of Nerve Axion diffusion equations

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171287000875 ◽

1987 ◽

Vol 10 (4) ◽

pp. 787-796

Author(s):

Rina Ling

Keyword(s):

Periodic Solutions ◽

Parabolic Equations ◽

Periodic Wave ◽

Diffusion Equations ◽

Stability Of Solutions ◽

Periodic Wave Solutions ◽

Wave Solutions ◽

Existence And Stability ◽

Systems Of Parabolic Equations

Unstable periodic solutions of systems of parabolic equations are studied. Special attention is given to the existence and stability of solutions.

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Almost-periodic solutions of elliptic and parabolic equations in unbounded domains

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500002110 ◽

2002 ◽

Vol 132 (6) ◽

pp. 1275-1306 ◽

Cited By ~ 1

Author(s):

M. Amar ◽

R. Gianni

Keyword(s):

Periodic Solutions ◽

Boundary Layers ◽

Parabolic Equations ◽

Existence And Uniqueness ◽

Unbounded Domains ◽

Parabolic Partial Differential Equations ◽

Almost Periodic Solutions ◽

Almost Periodic ◽

Periodic Homogenization ◽

Elliptic And Parabolic Equations

This paper is devoted to the study of the existence and uniqueness of almost-periodic solutions for elliptic and parabolic partial differential equations in unbounded domains. This kind of investigation had originally been motivated by the study of the so-called boundary layers, whose behaviour is crucial in the framework of periodic homogenization.

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Stability in 𝐿𝑞-norm for inverse source parabolic problems

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2019-0081 ◽

2020 ◽

Vol 28 (6) ◽

pp. 797-814

Author(s):

Elena-Alexandra Melnig

Keyword(s):

Parabolic Equations ◽

Main Tool ◽

Parabolic Systems ◽

Carleman Estimates ◽

Parabolic Problems ◽

Lebesgue Spaces ◽

First Order ◽

Lipschitz Estimates ◽

Systems Of Parabolic Equations

AbstractWe consider systems of parabolic equations coupled in zero and first order terms. We establish Lipschitz estimates in {L^{q}}-norms, {2\leq q\leq\infty}, for the source in terms of the solution in a subdomain. The main tool is a family of appropriate Carleman estimates with general weights, in Lebesgue spaces, for nonhomogeneous parabolic systems.

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