## Partial Differential Equations: Models in Physics and BiologyThis volume contains the contributions of the conference "Partial Differential Equations" in Han-sur-Lesse, Belgium, December 1993. The originally intended Belgian-French meeting developed into a truely international conference, including specialists from Argentina, Germany, Puerto Rico, Russia, Spain, and the USA. The authors was to discuss a variety of important questions in applied sciences, engineering and mathematical physics which lead to deep structures and new challenges to the analysis of partial differential equations. The articles show the complexity of phenomena for a broader readership in non-linear analysis, free boundary value problems, effects from singularities, asymptotics, and stability of solutions. |

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### Contents

On the intersections of Wiener sausages | 9 |

Characterization of iterated powers | 40 |

Some results in stochastic spectral | 56 |

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algebra analytic apply assume asymptotic expansion asymptotic solution Banach space boundary conditions boundary value problems bounded Brownian motion Casteren Cauchy problem classical solution coefficients compact consider constant continuous convergence Corollary corresponding defined definition denote differential equations differential operators Dirichlet domain edge elliptic elliptic operators estimate exists finite formula function f(x G D(A given Hence Hilbert space homogeneous homogeneous function implies inequality integrated cosine function intersection K0+V Lemma linear operators manifold mapping Math Mathematics microfunctions Moreover neighbourhood nonlinear norm obtain paper Partial Differential Equations principal eigenvalue proof of Theorem properties Proposition prove pseudo-differential operators Remark respect result resurgent function satisfies Schulze semigroups sequence Sobolev spaces Stokes directions subspace Suppose symbol Theorem 1.1 theory trace class transform unique variables vector weight Wiener sausages