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Some Exact Self-Similar Solutions to a Density-Dependent Reaction-Diffusion Model
Exact Self-Similar Density-Dependent Reaction-Diffusion Model Biological Physics
2012/4/20
In this paper, we investigated a density-dependent reaction-diffusion equation, $u_t = (u^{m})_{xx} + u - u^{m}$. This equation is known as the extension of the Fisher or Kolmogoroff-Petrovsky-Piscoun...
Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
Local-in-space estimates initial time weak solutions of the Navier-Stokes equations forward self-similar solutions Analysis of PDEs
2012/4/18
We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with $(-1)$-homogeneous initial data has a global scale-invariant solution which is smooth for positive time...
Exponential self similar solutions technique for instability phenomenon arising in double phase flow through porous medium with capillary pressure
Immiscible fluid Instability Flows in porous media
2010/9/25
The theoretical studies involved development of the differential equations which describe the instability of water by an oil-saturated rock. The basic assumption underlying the present investigation i...
Kinematic Self-Similar Solutions of Locally Rotationally Symmetric Spacetimes
Locally rotationally symmetric Self-similarity
2010/6/30
This paper contains locally rotationally symmetric kinematic self-similar perfect fluid and dust solutions. We consider three families of metrics which admit kinematic self-similar vectors of the firs...
Remarks on self-similar solutions to the compressible Navier-Stokes equations of a 1D viscous polytropic ideal gas
self-similar solutions Navier-Stokes equations viscous polytropic gas
2010/9/13
This paper is concerned with the self-similar solutions to the compressible Navier-Stokes equations of a 1D viscous polytropic ideal gas. Our results show that there exist neither forward nor backward...