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Radial equivalence and applications to the qualitative theory for a class of non-homogeneous reaction-diffusion equations
  • Razvan Gabriel Iagar,
  • Ariel Sánchez
Razvan Gabriel Iagar
Universidad Rey Juan Carlos Departamento Matematica Aplicada Ciencia e Ingenieria de los Materiales y Tecnologia Electronica

Corresponding Author:[email protected]

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Ariel Sánchez
Universidad Rey Juan Carlos Departamento Matematica Aplicada Ciencia e Ingenieria de los Materiales y Tecnologia Electronica
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Abstract

Some transformations acting on radially symmetric solutions to the following class of non-homogeneous reaction-diffusion equations | x | σ 1 ∂ t u = ∆ u m + | x | σ 2 u p , ( x , t ) ∈ R N × ( 0 , ∞ ) , which has been proposed in a number of previous mathematical works as well as in several physical models, are introduced. We consider here m≥1, p≥1, N≥1 and σ 1 , σ 2 real exponents. We apply these transformations in connection to previous results on the one hand to deduce general qualitative properties of radially symmetric solutions and on the other hand to construct self-similar solutions which are expected to be patterns for the dynamics of the equations, strongly improving the existing theory. We also introduce mappings between solutions which work in the semilinear case m=1.
20 Dec 2022Submitted to Mathematical Methods in the Applied Sciences
21 Dec 2022Submission Checks Completed
21 Dec 2022Assigned to Editor
26 Dec 2022Review(s) Completed, Editorial Evaluation Pending
24 Jan 2023Reviewer(s) Assigned
02 May 2023Editorial Decision: Revise Minor
03 May 20231st Revision Received
10 May 2023Submission Checks Completed
10 May 2023Assigned to Editor
10 May 2023Review(s) Completed, Editorial Evaluation Pending
10 May 2023Reviewer(s) Assigned
12 May 2023Editorial Decision: Accept