Displaying 41 – 60 of 128

Showing per page

Fundamental solutions and asymptotic behaviour for the p-Laplacian equation.

Soshana Kamin, Juan Luis Vázquez (1988)

Revista Matemática Iberoamericana

We establish the uniqueness of fundamental solutions to the p-Laplacian equationut = div (|Du|p-2 Du),   p > 2,defined for x ∈ RN, 0 < t < T. We derive from this result the asymptotic behavoir of nonnegative solutions with finite mass, i.e., such that u(*,t) ∈ L1(RN). Our methods also apply to the porous medium equationut = ∆(um),   m > 1,giving new and simpler proofs of known results. We finally introduce yet another method of proving asymptotic results based on the...

Fundamental solutions and singular shocks in scalar conservation laws.

Emmanuel Chasseigne (2003)

Revista Matemática Complutense

We study the existence and non-existence of fundamental solutions for the scalar conservation laws ut + f(u)x = 0, related to convexity assumptions on f. We also study the limits of those solutions as the initial mass goes to infinity. We especially prove the existence of so-called Friendly Giants and Infinite Shock Solutions according to the convexity of f, which generalize the explicit power case f(u) = um. We introduce an extended notion of solution and entropy criterion to allow infinite shocks...

Gaussian estimates for fundamental solutions to certain parabolic systems.

Steve Hofmann, Seick Kim (2004)

Publicacions Matemàtiques

Auscher proved Gaussian upper bound estimates for the fundamental solutions to parabolic equations with complex coefficients in the case when coefficients are time-independent and a small perturbation of real coefficients. We prove the equivalence between the local boundedness property of solutions to a parabolic system and a Gaussian upper bound for its fundamental matrix. As a consequence, we extend Auscher's result to the time dependent case.

Gaussian estimates for Schrödinger perturbations

Krzysztof Bogdan, Karol Szczypkowski (2014)

Studia Mathematica

We propose a new general method of estimating Schrödinger perturbations of transition densities using an auxiliary transition density as a majorant of the perturbation series. We present applications to Gaussian bounds by proving an optimal inequality involving four Gaussian kernels, which we call the 4G Theorem. The applications come with honest control of constants in estimates of Schrödinger perturbations of Gaussian-type heat kernels and also allow for specific non-Kato perturbations.

Currently displaying 41 – 60 of 128