Results 41 to 50 of about 1,356,954 (292)
Impulsive Quenching for Degenerate Parabolic Equations
Journal of Mathematical Analysis and Applications, 1996 An impulsive problem for a singular degenerate parabolic equation is studied. Sufficient conditions for the existence of a unique critical length are given. The critical length \(a^*\) is the length of the space interval such that the solution with zero initial and boundary data quenches for intervals larger than \(a^*\) but it exists globally for ...
Chan, C.Y., Kong, P.C.
openaire +2 more sources
Discontinuous “viscosity” solutions of a degenerate parabolic equation [PDF]
Transactions of the American Mathematical Society, 1990 We study a nonlinear degenerate parabolic equation of the second order. Regularizing the equation by adding some artificial viscosity, we construct a generalized solution. We show that this solution is not necessarily continuous at all points.
BERTSCH, MICHIEL, Dal Passo R, Ughi, M.
openaire +4 more sources
Hölder gradient estimates for a class of singular or degenerate parabolic equations
Advances in Nonlinear Analysis, 2017 We prove interior Hölder estimates for the spatial gradients of the viscosity solutions to the singular or degenerate parabolic ...
Imbert Cyril +2 more
doaj +1 more source
Stochastic PDEs with multiscale structure [PDF]
, 2012 We study the spatial homogenisation of parabolic linear stochastic PDEs exhibiting a two-scale structure both at the level of the linear operator and at the level of the Gaussian driving noise.
Martin Hairer +3 more
core +1 more source
Admissible conditions for parabolic equations degenerating at infinity [PDF]
St. Petersburg Mathematical Journal, 2008 From the introduction: We investigate existence and uniqueness for bounded solutions of the parabolic Cauchy problem \[ \begin{aligned} \rho\partial_tu= \Delta u\quad &\text{in }\mathbb{R}^n\times \mathbb{R}_+:= S,\\ u= u_0\quad &\text{in }\mathbb{R}^n\times \{0\}\;(n\geq 3).\end{aligned}\tag{1.1} \] Concerning the coefficient \(\rho= \rho(x)\) and the
KAMIN S +2 more
openaire +2 more sources
Continuous dependence for BV-entropy solutions to strongly degenerate parabolic equations with variable coefficients [PDF]
, 1999 summary:We consider the Cauchy problem for degenerate parabolic equations with variable coefficients. The equation has nonlinear convective term and degenerate diffusion term which depends on the spatial and time variables.
Carrillo Menéndez, José +1 more
core +1 more source
PERIODIC SOLUTION FOR A CLASS OF DOUBLY DEGENERATE PARABOLIC EQUATION WITH NEUMANN PROBLEM [PDF]
مجلة جامعة الانبار للعلوم الصرفة, 2015 In this article, we study the periodic solution for a class of doubly degenerate parabolic equation with nonlocal terms and Neumann boundary conditions. By using the theory of Leray-Schauder degree, we obtain the existence of nontrivial nonnegative time ...
Raad Awad Hameed, Wafaa M. Taha
doaj +1 more source
Karpatsʹkì Matematičnì Publìkacìï, 2014 The paper found the explicit form of the fundamental solution of Cauchy problem for the equation of Kolmogorov type that has a finite number groups of spatial variables which are degenerate parabolic.
H.P. Malytska, I.V. Burtnyak
doaj +1 more source
Expansion of positivity to a class of doubly nonlinear parabolic equations
Electronic Journal of Qualitative Theory of Differential Equations, 2022 We establish the expansion of positivity of the nonnegative, local, weak solutions to the class of doubly nonlinear parabolic equations $$\partial_t (u^{q}) -\operatorname{div}{(|D u|^{p-2} D u)}=0, \qquad\ p>1 \ \text{and} \ q>0$$ considering ...
Eurica Henriques
doaj +1 more source
Stability for degenerate parabolic equations [PDF]
Advances in Calculus of Variations, 2010 The authors study the stability of the solutions of the evolutionary \(p\)-Laplace equation \[ {\partial u\over\partial t}= \nabla\cdot(|\nabla u|^{p-2}\nabla u) \] under variations of the parameter \(p\). The problem is delicate, since the underlying Sobolev space varieties with \(p\). The boundary values are given on the parabolic boundary of a space-
Parviainen, Mikko, Kinnunen, Juha
openaire +4 more sources