منابع مشابه
Generalized Gross heat equation with noises
In this paper we study the Gross heat equation perturbed by noises with the initial condition being a generalized function. The noises are given by either a white noise or a space-time white noise. The main technique we use is the representation of the Gross Laplacian as a convolution operator. It enables us to apply the convolution calculus on a suitable distribution space to obtain the explic...
متن کاملGeneralized Hermite Polynomials and the Heat Equation for Dunkl Operators
Based on the theory of Dunkl operators, this paper presents a general concept of multivariable Hermite polynomials and Hermite functions which are associated with finite reflection groups on R . The definition and properties of these generalized Hermite systems extend naturally those of their classical counterparts; partial derivatives and the usual exponential kernel are here replaced by Dunkl...
متن کاملOn the generalized Jacobi equation
The standard text-book Jacobi equation (equation of geodesic deviation) arises by linearizing the geodesic equation around some chosen geodesic, where the linearization is done with respect to the coordinates and the velocities. The generalized Jacobi equation, introduced by Hodgkinson in 1972 and further developed by Mashhoon and others, arises if the linearization is done only with respect to...
متن کاملA blow-up result for nonlinear generalized heat equation
Available online xxxx Keywords: Nonlinear heat equation Blow up Sobolev spaces with variable exponents a b s t r a c t In this paper we consider a nonlinear heat equation with nonlinearities of variable-exponent type. We show that any solution with nontrivial initial datum blows up in finite time. We also give a two-dimension numerical example to illustrate our result.
متن کاملThe Heat Equation on Discrete Domains
In this paper, we will explore the properties of the Heat Equation on Discrete Networks, laying out groundwork and giving general forms for solutions, and then exploring the inverse problem. We will also focus on comparisons of Heat Networks with Electrical and Random-Walk Networks.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1984
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500022392