Asymptotic stability of traveling wave solutions for nonlocal viscous conservation laws with explicit decay rates [PDF]
, 2017 We consider scalar conservation laws with nonlocal diffusion of Riesz-Feller type such as the fractal Burgers equation. The existence of traveling wave solutions with monotone decreasing profile has been established recently (in special cases).
Achleitner, Franz, Ueda, Yoshihiro
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Traveling wave solution of the Hele-Shaw model of tumor growth with nutrient [PDF]
, 2014 Several mathematical models of tumor growth are now commonly used to explain medical observations and predict cancer evolution based on images. These models incorporate mechanical laws for tissue compression combined with rules for nutrients availability
Perthame, Benoît +2 more
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Partial Differential Equations in Applied Mathematics, 2023 In a range of nonlinear fields, for example molecular biology, physics in plasma, quantum mechanics, elastic media, nonlinear optics, the surface of water waves, and others, many complicated nonlinear behaviors can be pronounced using nonlinear ...
U.H.M. Zaman +3 more
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A Hamilton-Jacobi approach for front propagation in kinetic equations [PDF]
, 2014 In this paper we use the theory of viscosity solutions for Hamilton-Jacobi equations to study propagation phenomena in kinetic equations. We perform the hydrodynamic limit of some kinetic models thanks to an adapted WKB ansatz.
Bouin, Emeric
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Homoclinic and heteroclinic solutions to a hepatitis C evolution model
Open Mathematics, 2018 Homoclinic and heteroclinic solutions to a standard hepatitis C virus (HCV) evolution model described by T. C. Reluga, H. Dahari and A. S. Perelson, (SIAM J. Appl. Math., 69 (2009), pp. 999–1023) are considered in this paper.
Telksnys Tadas +4 more
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Exact solutions for the ion sound Langmuir wave model by using two novel analytical methods
Results in Physics, 2020 In the present paper, the system of equations for the ion sound and Langmuir waves (SEISLWs) is considered to obtain the new solitary wave solutions of the non-linear evolution equations. Here, we used the relatively two new analytical methods to achieve
A. Tripathy, S. Sahoo
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(Non)linear instability of periodic traveling waves: Klein–Gordon and KdV type equations
Advances in Nonlinear Analysis, 2014 We prove the existence and nonlinear instability of periodic traveling wave solutions for the critical one-dimensional Klein–Gordon equation. We also establish a linear instability criterium for a KdV type system.
Angulo Pava Jaime, Natali Fabio
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Traveling gravity water waves with critical layers [PDF]
, 2016 We establish the existence of small-amplitude uni- and bimodal steady periodic gravity waves with an affine vorticity distribution, using a bifurcation argument that differs slightly from earlier theory.
Aasen, Ailo, Varholm, Kristoffer
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Travelling waves in a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypical trait [PDF]
, 2012 We consider a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypical trait. To sustain the possibility of invasion in the case where an underlying principal eigenvalue is negative, we ...
Alfaro, Matthieu +2 more
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Generalized transition fronts for one-dimensional almost periodic Fisher-KPP equations [PDF]
, 2016 This paper investigates the existence of generalized transition fronts for Fisher-KPP equations in one-dimensional, almost periodic media. Assuming that the linearized elliptic operator near the unstable steady state admits an almost periodic ...
Nadin, Grégoire, Rossi, Luca
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