Existence of a Global Solution for a Viscoelastic System
Copyright policy )Existence of a Global Solution for a Viscoelastic System
The author considers the Cauchy problem for the viscoelastic system \[ v_t- u_x= 0,\quad u_t- f(v)_x+ ku= u_{xx} \] without the restriction that the initial data approach constants at infinity. Existence of unique classical solution is proved, including a priori estimates. A parallel result for a model of compressible adiabatic flow through porous media with a physical viscosity is also obtained.
- Academia Sinica Taiwan
- Wuhan Institute of Physics and Mathematics China (People's Republic of)
- Wuhan Institute of Physics and Mathematics China (People's Republic of)
- International School for Advanced Studies Italy
- Institute Academy for Precision Measurment Science and Technology, CAS China (People's Republic of)
Cauchy problem, a priori estimates, Flows in porous media; filtration; seepage, Applied Mathematics, Dynamical problems in solid mechanics, PDEs in connection with fluid mechanics, Analysis, existence of unique classical solution
Cauchy problem, a priori estimates, Flows in porous media; filtration; seepage, Applied Mathematics, Dynamical problems in solid mechanics, PDEs in connection with fluid mechanics, Analysis, existence of unique classical solution
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