Front propagation in nonlinear parabolic equations
نویسندگان
چکیده
We study existence and stability of travelling waves for nonlinear convection diffusion equations in the 1-D Euclidean space. The diffusion coefficient depends on the gradient in analogy with the p-Laplacian and may be degenerate. Unconditional stability is established with respect to initial data perturbations in L(R). Running head: Poincaré inequality and P.-S. condition
منابع مشابه
Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations
In this article, we provide existence results for a general class of nonlocal and nonlinear second-order parabolic equations. The main motivation comes from front propagation theory in the cases when the normal velocity depends on the moving front in a nonlocal way. Among applications, we present level-set equations appearing in dislocations’ theory and in the study of Fitzhugh-Nagumo systems.
متن کاملMini - workshop “ Recent Trends in Traveling Waves ”
10:00~10:40 Danielle Hilhorst (CNRS / Univ. Paris-Sud) Front propagation in nonlinear parabolic equations 11:00~11:40 Thomas Giletti (University of Lorraine) Speed-up of propagation by a road – the periodically heterogeneous framework 11:50~12:30 Masaharu Taniguchi (Okayama University) An (N −1)-dimensional convex compact set gives an N -dimensional traveling front in the Allen-Cahn equation 12...
متن کاملEstimates on Front Propagation for Nonlinear Higher-order Parabolic Equations: an Algorithmic Approach
We present an algorithm for the derivation of lower bounds on support propagation for a certain class of nonlinear parabolic equations. We proceed by combining the ideas in some recent papers by the author with the algorithmic construction of entropies due to Jüngel and Matthes, reducing the problem to a quantifier elimination problem. Due to its complexity, the quantifier elimination problem c...
متن کاملMultiscale Approach to Parabolic Equations Derivation: Beyond the Linear Theory
The concept of the iterative parabolic approximation based on the multiscale technique is discussed. This approach is compared with the traditional ways to derive the wide-angle parabolic equation. While the latter fail in the nonlinear case, the multiscale derivation technique leading to iterative parabolic equations can be easily adapted to handle it. The nonlinear iterative parabolic approxi...
متن کاملFormation of discontinuities in flux-saturated degenerate parabolic equations
We endow the nonlinear degenerate parabolic equation used to describe propagation of thermal waves in plasma or in a porous medium, with a mechanism for flux saturation intended to correct the nonphysical gradientflux relations at high gradients. We study both analytically and numerically the resulting equation: ut = [uQ(g(u)x)]x, n > 0, where Q is a bounded increasing function. This model reve...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. London Math. Society
دوره 90 شماره
صفحات -
تاریخ انتشار 2014