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We considered classical solutions to the initial boundary value problem fornon-isentropic compressible Euler equations with damping in multi-dimensions.We obtained global a priori estimates and global existence results of classicalsolutions to both non-isentropic Euler equations with damping and theirnonlinear diffusion equations under small data assumption. We proved thepressure and velocity decay exponentially to constants, while the entropy anddensity can not approach constants. Finally, we proved the pressure andvelocity of the non-isentropic Euler equations with damping convergeexponentially to those of their nonlinear diffusion equations when the timegoes to infinity.

Global Existence and Nonlinear Diffusion of Classical Solutions to Non-Isentropic Euler Equations with Damping in Bounded Domain