Asymptotic Speed of Propagation for Fisher-Type Degenerate Reaction-Diffusion-Convection Equations

2010 ◽  
Vol 10 (3) ◽  
Author(s):  
Luisa Malaguti ◽  
Stefano Ruggerini
Keyword(s):  
Initial Value Problem ◽  
Reaction Diffusion ◽  
Initial Condition ◽  
Initial Value ◽  
Convection Equation ◽  
All Solutions ◽  
Asymptotic Speed ◽  
Speed Of Propagation ◽  
Diffusion Convection

AbstractThe paper deals with the initial value problem for the degenerate reaction-diffusion-convection equationuwhere h is continuous, m > 1, and f is of Fisher-type. By means of comparison type techniques, we prove that the equilibrium u ≡ 1 is an attractor for all solutions with a continuous, bounded, non-negative initial condition u

Finite Speed of Propagation in Monostable Degenerate Reaction-Diffusion-Convection Equations

2005 ◽  
Vol 5 (2) ◽  
Author(s):  
Luisa Malaguti ◽  
Cristina Marcelli
Keyword(s):  
Reaction Diffusion ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Finite Speed Of Propagation ◽  
Finite Speed ◽  
Wave Solutions ◽  
Convection Equation ◽  
Speed Of Propagation ◽  
Diffusion Convection

AbstractWe study the existence and properties of travelling wave solutions of the Fisher-KPP reaction-diffusion-convection equation u

scholarly journals Existence and uniqueness of analytic solutions of the Shabat equation

2005 ◽  
Vol 2005 (8) ◽  
pp. 855-862 ◽  
Author(s):  
Eugenia N. Petropoulou
Keyword(s):  
Upper Bound ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Analytic Solution ◽  
Sufficient Conditions ◽  
Analytic Solutions ◽  
Initial Condition ◽  
Initial Value ◽  
First Derivative

Sufficient conditions are given so that the initial value problem for the Shabat equation has a unique analytic solution, which, together with its first derivative, converges absolutely forz∈ℂ:|z|<T,T>0. Moreover, a bound of this solution is given. The sufficient conditions involve only the initial condition, the parameters of the equation, andT. Furthermore, from these conditions, one can obtain an upper bound forT. Our results are in consistence with some recently found results.

scholarly journals Analysis of the Boundary Value and Control Problems for Nonlinear Reaction–Diffusion–Convection Equation

2001 ◽  
Vol 14 (4) ◽  
pp. 452-462
Author(s):  
Gennady V. Alekseev ◽  
Keyword(s):  
Boundary Value Problem ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Reaction Diffusion ◽  
Control Problems ◽  
Stability Estimates ◽  
Convection Equation ◽  
Reaction Coefficient ◽  
Diffusion Convection ◽  
And Control

The global solvability of the inhomogeneous mixed boundary value problem and control problems for the reaction–diffusion–convection equation are proved in the case when the reaction coefficient nonlinearly depends on the concentration. The maximum and minimum principles are established for the solution of the boundary value problem. The optimality systems are derived and the local stability estimates of optimal solutions are established for control problems with specific reaction coefficients

Wave propagation in a thin-walled liquid-filled initially stressed tube

1984 ◽  
Vol 141 ◽  
pp. 289-308 ◽  
Author(s):  
G. D. C. Kuiken
Keyword(s):  
Blood Pressure ◽  
Wave Propagation ◽  
Dispersion Equation ◽  
Newtonian Fluid ◽  
Initial Value Problem ◽  
Wave Mode ◽  
Initial Value ◽  
Thin Walled ◽  
Speed Of Propagation ◽  
Infinite Tube

Wave propagation through a thin-walled cylindrical orthotropic viscoelastic initially stressed tube filled with a Newtonian fluid is discussed. Special attention is drawn to the influence of the initial stretch on the wave propagation. It is shown that initial stretching of real arteries enhances the propagation of blood pressure pulses in mammalian arteries. The dispersion equation for the initial-value problem of a semi-infinite tube is also derived. It is shown that the speed of propagation and the attenuation vary with the distance from the support. The results obtained for the axial wave mode provide an explanation for the experimental observations, which is not possible with the results obtained for the infinite tube.

Sign in / Sign up

Export Citation Format

Share Document