Initial values for parabolic functions

Initial - Boundary Value Problems for Parabolic Equations

The Parabolic Logistic Equation with Blow-up Initial and Boundary Values

In this article, we investigate the parabolic logistic equation with blow-up initial and boundary values over a smooth bounded domain Ω: ( ut −∆u = a(x, t)u− b(x, t)u in Ω× (0, T ), u =∞ on ∂Ω× (0, T ) ∪ Ω× {0}, where T > 0 and p > 1 are constants, a and b are continuous functions, with b > 0 in Ω × [0, T ), b(x, T ) ≡ 0. We study the existence and uniqueness of positive solutions, and their as...

THE COMPARISON OF EFFICIENT RADIAL BASIS FUNCTIONS COLLOCATION METHODS FOR NUMERICAL SOLUTION OF THE PARABOLIC PDE’S

In this paper, we apply the compare the collocation methods of meshfree RBF over differential equation containing partial derivation of one dimension time dependent with a compound boundary nonlocal condition.

Singular values of convex functions of matrices

‎Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $‎sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $‎sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$  are nonzero matrices and each $X_{i}$ is‎ ‎positive semidefinite‎. ‎It is shown that if $f$ is a nonnegative increasing ‎convex function on $left[ 0,infty right) $ satisfying $fleft( 0right)‎ ‎=0 $‎, ‎then  $$‎2s_{j}left( fleft( fra...

Degenerate Parabolic Initial-Boundary Value Problems*

in Hilbert space and their realizations in function spaces as initial-boundary value problems for partial differential equations which may contain degenerate or singular coefficients. The Cauchy problem consists of solving (1.1) subject to the initial condition Jdu(0) = h. We are concerned with the case where the solution is given by an analytic semigroup; it is this sense in which the Canchy p...