1,721,004 research outputs found
On the Classical Solutions for the Kuramoto-Sivashinsky Equation with Ehrilch-Schwoebel Effects
No full textThe Kuramoto-Sivashinsky equation with Ehrilch-Schwoebel effects models the evolution of surface morphology during Molecular Beam Epitaxy growth, provoked by an interplay between deposition of atoms onto the surface and the relaxation of the surface profile through surface diffusion. It consists of a nonlinear fourth order partial differential equation. Using energy methods we prove the well-posedness (i.e.. existence, uniqueness and stability with respect to the initial data) of the classical solutions for the Cauchy problem, associated with this equation
ON A DIFFUSION MODEL FOR GROWTH AND DISPERSAL IN A POPULATION
No full textIn this paper, we prove the wellposedness of the classical solutions for the equation, deduced in [23]. It represents a reaction-diffusion model in which spatial structure is maintained by means of a diffusive mechanism more general than classical Fickian diffusion. This generalized diffusion takes into account the diffusive gradient (or gradient energy) necessary to maintain a pattern even in a single diffusing species
The Serra della Fastuca Tephra at Pantelleria: physical parameters for an explosive eruption of peralkaline magma.
No full textA singular limit problem for conservation laws related to the Rosenau-Korteweg-de Vries equation
Full text linkWe consider the Rosenau-Korteweg-de Vries equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Burgers equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method
A singular limit problem for conservation laws related to the Kawahara-Korteweg-de Vries equation
No full textWeconsidertheKawahara-Korteweg-deVriesequation,whichcon- tains nonlinear dispersive effects. We prove that as the dispersion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Burgers equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L^p setting
Wellposedness results for the Short Pulse Equation
No full textThe short pulse equation provides a model for the propagation of ultra-short light pulses in silica optical fibers. It is a nonlinear evolution equation.
In this paper the wellposedness of bounded solutions for the homogeneous initial boundary value problem and the Cauchy problem associated to this equation are studied
WELLPOSEDNESS OF BOUNDED SOLUTIONS OF THE NON-HOMOGENEOUS INITIAL BOUNDARY FOR THE SHORT PULSE EQUATION
No full textThe short pulse equation provides a model for the propagation of ultra-short light pulses in silica optical fibers. It is a nonlinear evolution equation.
In this paper the wellposedness of bounded solutions for the inhomogeneous initial boundary value problem associated to this equation is studied
Oleinik type estimates for the Ostrovsky–Hunter Equation
No full textThe Ostrovsky-Hunter equation provides a model for small-amplitude long waves in
a rotating fluid of finite depth. It is a nonlinear evolution equation. In this paper we study the well-posedness for the Cauchy problem associated to this equation with a class of bounded discontinuous solutions.
We show that we can replace the Kruzkov-type entropy inequalities by an Oleinik-type estimate and to prove uniqueness
via a nonlocal adjoint problem. An implication is that a shock wave in an entropy weak solution to the
Ostrovsky-Hunter equation is admissible only if it jumps down in value (like the inviscid Burgers equation)
On the Wellposedness of the exp-Rabelo equation
No full textThe exp-Rabelo equation describes pseudo-spherical surfaces. It is a nonlinear evolution equation.
In this paper the wellposedness of bounded from above solutions for the initial value problem associated to this equation is studied
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