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

• Autorzy: Arkadiusz Szymaniec
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35A01: Existence problems: global existence, local existence, non-existence
• 35G25: Initial value problems for nonlinear higher-order equations
• 35G16: Initial-boundary value problems for linear higher-order equations
• 35A02: Uniqueness problems: global uniqueness, local uniqueness, non-uniqueness
• 35G55: Initial value problems for nonlinear higher-order systems
• 35C20: Asymptotic expansions
• 35M13: Initial-boundary value problems for equations of mixed type

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2010
• Tom: 37
• Numer: 4
• Strony: 437-458

Daty

wydano

2010

Twórcy

autor

Arkadiusz Szymaniec

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

Identyfikatory

DOI

10.4064/am37-4-4