In this book a hierarchy of macroscopic models for semiconductor devices is presented.
Three classes of models are studied in detail: isentropic drift-diffusion equations, energy …

The subject of blow-up in a finite time, or at least very rapid growth, of a solution to a partial
differential equation has been an area of intense re search activity in mathematics. Some …

Unique existence of solutions to porous media equations driven by continuous linear
multiplicative space–time rough signals is proven for initial data in L^1(O) on bounded …

We establish local existence and comparison for a model problem which incorporates the
effects of non‐linear diffusion, convection and reaction. The reaction term to be considered …

The main focus of this study was to develop a numerical scheme with new expressions for
interface flux approximations based on the upwind approach in the finite volume method …

It has long been known that the heat equation displays infinite speed of propagation. This is
to say that if the initial data are nonnegative and have nonempty compact support, the …

In this paper, we establish the local existence of the solution and the finite time blow-up
result for the equationv τ= v mxx+ a∫ l− lv qdx, x∈− l, l, τ> 0. Moreover, it is proved that the …

This paper investigates the blow-up and global existence of nonnegative solutions of the
system [Formula: see text] with homogeneous Dirichlet boundary data, where Ω⊂ RN is a …

Roles of weight functions to a nonlinear porous medium equation with nonlocal source and
nonlocal boundary condition Page 1 J. Math. Anal. Appl. 342 (2008) 559–570 www.elsevier.com/locate/jmaa …

Blowup of solutions to a porous medium equation with nonlocal boundary condition -
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