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**publisher and metadata sources**).We consider the semilinear parabolic system
(S) { ut-Δu=vp ; vt-Δv=uq,
where x Є R(N) (N ≥ 1), t > 0, and p, q are positive real numbers. At t=0, nonnegative, continuous, and bounded initial… Continue Reading

Abstract We describe the large time behavior of solutions of the convection-diffusion equation u t − Δu = a · ▽(¦u¦ q − 1 u) in (0, ∞) × R N with a ϵ R N and q ⩾ 1 + 1 N , N ⩾ 1 . When q = 1 + 1 N ,… Continue Reading

A system for heating objects by means of microwave energy in an assembly line fashion is disclosed herein and utilizes a specific microwave oven assembly especially suitable for this purpose. The… Continue Reading

Abstract The occurrence of gelation and the existence of mass-conserving solutions to the continuous coagulation–fragmentation equation are investigated under various assumptions on the coagulation… Continue Reading

On demontre l'existence, l'unicite et la regularite de solutions globales pour le probleme de Cauchy: u t −Δu=u p dans (o,∞)×R n , u(o,x)=u 0 (x)≥0 dans R n , u≥0 dans (o,∞)×R n avec donnee initiale… Continue Reading

We consider the Cauchy problem for the following scalar conservation law with partial viscosity ut = A, u + 0 (f(u)), (x, y) E R N, t > O. The existence of solutions is proved by the vanishing… Continue Reading

Abstract We prove existence and uniqueness of the solution of a homogeneous quantum Boltzmann equation describing the photon–electron interaction. We study the asymptotic behaviour of the solutions,… Continue Reading

Local and global well-posedness for the Cauchy problem associated with the nonlinear Dirac equation $$ i{\partial \psi \over \partial t}+i\alpha \cdot\nabla \psi -m\beta \psi +G(\psi)=0\quad \hbox{...