Qualitative properties of solutions to mixed-diffusion bistable equations
نویسندگان
چکیده
منابع مشابه
Qualitative Properties of Saddle-shaped Solutions to Bistable Diffusion Equations
We consider the elliptic equation −∆u = f(u) in the whole R , where f is of bistable type. It is known that there exists a saddleshaped solution in R. This is a solution which changes sign in R and vanishes only on the Simons cone C = {(x, x) ∈ R×R : |x| = |x|}. It is also known that these solutions are unstable in dimensions 2 and 4. In this article we establish that when 2m = 6 every saddle-s...
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We consider a bistable differential-difference equation with inhomogeneous diffusion. Employing a piecewise linear nonlinearity, often referred to as McKean’s caricature of the cubic, we construct front solutions which correspond, in the case of homogeneous diffusion, to monotone traveling front solutions or stationary front solutions in the case of propagation failure. A general form for these...
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متن کاملSaddle-shaped Solutions of Bistable Diffusion Equations in All of R
We study the existence and instability properties of saddleshaped solutions of the semilinear elliptic equation −∆u = f(u) in the whole R, where f is of bistable type. It is known that in dimension 2m = 2 there exists a saddle-shaped solution. This is a solution which changes sign in R and vanishes only on {|x1| = |x2|}. It is also known that this solution is unstable. In this article we prove ...
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ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2016
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-016-0987-6