Results 231 to 240 of about 15,297,882 (275)

Estimates for Fundamental Solutions of Second-Order Parabolic Equations

Journal of the London Mathematical Society, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liskevich, V, Semenov, Yu
openaire   +2 more sources

Homogenization for Degenerate Quasilinear Parabolic Equations of Second Order

Acta Mathematicae Applicatae Sinica, English Series, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Xingyou, Huang, Yong
openaire   +2 more sources

Removable singularities of solutions of second-order parabolic equations

Mathematical Notes of the Academy of Sciences of the USSR, 1991
Let \({\mathcal L}\) denote a scalar linear second order parabolic operator on a bounded cylindrical domain \(Q\). Central in the paper is the notion of a set removable in a functional space \(Y\). By definition, it is a compact set \(E\subset Q\) such that if \(u\in Y\) is a weak solution of \({\mathcal L}u=0\) in \(Q\backslash E\) then necessarily ...
openaire   +1 more source

LINEAR EQUATIONS OF THE SECOND ORDER OF PARABOLIC TYPE

Russian Mathematical Surveys, 1962
CONTENTSIntroduction § 1. The maximum principle. Uniqueness of the solutions of the basic boundary value problems § 2. A priori estimates § 3. Solution of boundary value problems by Rothe's method. The Cauchy problem § 4. The fundamental solution of a linear parabolic equation. The Green's function.
A M Il'in, A S Kalashnikov, O A Oleinik
openaire   +1 more source

Generalized solutions of second order parabolic equations

1966
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ivanov, A. V., Ladyzhenskaya, O. A., Treskunov, A. L., Ural'tseva, N. N.   +3 more
openaire   +2 more sources

Ito’s Second Order Parabolic Equations

1990
0.1. Let us fix T 0, T∈R + with T 0 ≤ T, and d, d 1 ∈N. Suppose that a standard probability space \( = (\Omega ,{\cal F},{\{ {{\cal F}_{t}}\} _{{t \in [0,T]}}},) \) and a standard Wiener process ω(t) in \( {^{{{d_{1}}}}} \) on this probability space are given.
openaire   +1 more source

Second-Order Linear Parabolic Equations

1983
Parabolic equations arise in diffusion processes, and more generally in “irreversible” time-dependent processes. Mathematically, this is reflected in the fact that the equations are not invariant under the reversal of time ; i.e., under the transformation t → —t. This means that knowledge about the “past” is lost as time increases.
openaire   +1 more source

On Properties of Solutions to Nonlinear Parabolic Equations of the Second Order

Journal of Dynamical and Control Systems, 1999
The author studies sufficient conditions for finite time blow-up of positive solutions of the equation \(u_t=Lu+a_0(x,t)u^{\sigma_1}\) in \(\Omega\times(0,T)\) satisfying the nonlinear boundary condition \({\partial u\over\partial\nu}=b_0(x,t)u^{\sigma_2}\).
openaire   +1 more source

Degenerate elliptic‐parabolic equations of second order

Communications on Pure and Applied Mathematics, 1967
Kohn, J. J., Nirenberg, Louis
openaire   +1 more source

Asymptotic behaviour of the fundamental solution of a second-order parabolic equation

Sbornik: Mathematics, 1995
Summary: We study the asymptotic behaviour as \(t \to \infty\) of the fundamental solution \(G(x,s,t)\) of the Cauchy problem for the parabolic equation \(G_t - G_{xx} + a(x)G = 0\), \(x \in \mathbb{R}^1\), \(t > 0\). We suppose that the coefficient \(a(x)\) can be written as \(x \to \pm \infty\) in the form \(a(x) = a_2^\pm x^{-2} + \varphi (x ...
openaire   +2 more sources