Global solution to the Cauchy problem of nonlinear thermodiffusion in a solid body

Volume 37 / 2010

Arkadiusz Szymaniec Applicationes Mathematicae 37 (2010), 437-458 MSC: 35G16, 35G25, 35G55, 35M13, 35A01, 35A02, 35C20. DOI: 10.4064/am37-4-4


We consider the initial-value problem for a nonlinear hyperbolic-parabolic system of three coupled partial differential equations of second order describing the process of thermodiffusion in a solid body (in one-dimensional space). We prove global (in time) existence and uniqueness of the solution to the initial-value problem for this nonlinear system. The global existence is proved using time decay estimates for the solution of the associated linearized problem. Next, we prove an energy estimate in Sobolev spaces with constant independent of time. Such an energy estimate allows us to apply the standard continuation argument to continue the local solution to be defined for all times.


  • Arkadiusz SzymaniecInstitute of Mathematics and Cryptology
    Faculty of Cybernetics
    Military University of Technology
    S. Kaliskiego 2
    00-908 Warszawa, Poland

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