Local existence and finite-time blow-up in multidimensional radiation hydrodynamics
نویسندگان
چکیده
We first prove the local existence of smooth solutions to the Cauchy problem for the equations of multidimensional radiation hydrodynamics which are a hyperbolicBoltzmann coupled system. Then, we show that a smooth solution will blow up in finite time if the initial data are large. Moreover, the property of finite propagation speed is obtained simultaneously.
منابع مشابه
Existence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation
In this paper, we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation. Moreover, the finite-time blow-up of the solution for the equation is investigated by the concavity method.
متن کاملFinite time blow up of solutions of the Kirchhoff-type equation with variable exponents
In this work, we investigate the following Kirchhoff-type equation with variable exponent nonlinearities u_{tt}-M(‖∇u‖²)△u+|u_{t}|^{p(x)-2}u_{t}=|u|^{q(x)-2}u. We proved the blow up of solutions in finite time by using modified energy functional method.
متن کاملA note on blow-up in parabolic equations with local and localized sources
This note deals with the systems of parabolic equations with local and localized sources involving $n$ components. We obtained the exponent regions, where $kin {1,2,cdots,n}$ components may blow up simultaneously while the other $(n-k)$ ones still remain bounded under suitable initial data. It is proved that different initial data can lead to different blow-up phenomena even in the same ...
متن کاملLocal Existence and Blow up in Nonlinear Thermoelasticity with Second Sound
In this work we establish a local existence and a blow up result for a multidimensional nonlinear system of thermoelasticity with second sound.
متن کاملOn certain time- and space-fractional evolution systems
In this paper, we investigate the local existence and the finite-time blow-up of solutions of semilinear parabolic system with nonlocal in time nonlinearity. In addition, we also give the blow-up rate and necessary conditions for local and global existence.
متن کامل