Displaying similar documents to “Behaviour of solutions to u t - Δ u + | ∇ u | p = 0 as p → +∞”

L ∞ -estimate for solutions of nonlinear parabolic systems

Wojciech Zajączkowski (1996)

Banach Center Publications

Similarity:

We prove existence of weak solutions to nonlinear parabolic systems with p-Laplacians terms in the principal part. Next, in the case of diagonal systems an L ∞ -estimate for weak solutions is shown under additional restrictive growth conditions. Finally, L ∞ -estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The L ∞ -estimates are obtained by the Di Benedetto methods.

Neumann problem for one-dimensional nonlinear thermoelasticity

Yoshihiro Shibata (1992)

Banach Center Publications

Similarity:

The global existence theorem of classical solutions for one-dimensional nonlinear thermoelasticity is proved for small and smooth initial data in the case of a bounded reference configuration for a homogeneous medium, considering the Neumann type boundary conditions: traction free and insulated. Moreover, the asymptotic behaviour of solutions is investigated.

Qualitative investigation of nonlinear differential equations describing infiltration of water

Xingbao Wu (1995)

Annales Polonici Mathematici

Similarity:

A nonlinear differential equation of the form (q(x)k(x)u')' = F(x,u,u') arising in models of infiltration of water is considered, together with the corresponding differential equation with a positive parameter λ, (q(x)k(x)u')' = λF(x,u,u'). The theorems about existence, uniqueness, boundedness of solution and its dependence on the parameter are established.

On a Theorem of Mierczyński

Gerd Herzog (1998)

Colloquium Mathematicae

Similarity:

We prove that the initial value problem x’(t) = f(t,x(t)), x ( 0 ) = x 1 is uniquely solvable in certain ordered Banach spaces if f is quasimonotone increasing with respect to x and f satisfies a one-sided Lipschitz condition with respect to a certain convex functional.

On a discrete version of the antipodal theorem

Krzysztof Oleszkiewicz (1996)

Fundamenta Mathematicae

Similarity:

The classical theorem of Borsuk and Ulam [2] says that for any continuous mapping f : S k → ℝ k there exists a point x ∈ S k such that f(-x) = f(x). In this note a discrete version of the antipodal theorem is proved in which S k is replaced by the set of vertices of a high-dimensional cube equipped with Hamming’s metric. In place of equality we obtain some optimal estimates of i n f x | | f ( x ) - f ( - x ) | | which were previously known (as far as the author knows) only for f linear (cf. [1]).

Carathéodory balls and norm balls in H p , n = z ∈ ℂ n : ∥ z ∥ p < 1

Binyamin Schwarz, Uri Srebro (1996)

Banach Center Publications

Similarity:

It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on H p , n = z ∈ ℂ n : ∥ z ∥ p < 1 which are balls with respect to the complex l p norm in ℂ n are those centered at the origin.

L ∞ -estimates for solutions of nonlinear parabolic systems with gradient linear growth

Wojciech Zajączkowski (1996)

Banach Center Publications

Similarity:

Existence of weak solutions and an L ∞ -estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The L ∞ -estimate is proved for equations with coefficients continuous with respect to x and t in the general main part, and for diagonal systems with coefficients satisfying the Carathéodory condition.