相关论文: Smoluchowski's coagulation equation: uniqueness, n…
We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski's coagulation equations for the solvable kernels K(x,y)=2, x+y and xy. We prove the uniform convergence of densities to the self-similar solution with…
The well-posedness of the growth-coagulation equation is established for coagulation kernels having singularity near the origin and growing atmost linearly at infinity. The existence of weak solutions is shown by means of the method of the…
This contribution is concerned with the effective viscosity problem, that is, the homogenization of the steady Stokes system with a random array of rigid particles, for which the main difficulty is the treatment of close particles. Standard…
We consider Smoluchowski's coagulation equation with kernels of homogeneity one of the form $K_{\varepsilon }(\xi,\eta) =\big( \xi^{1-\varepsilon }+\eta^{1-\varepsilon }\big)\big ( \xi\eta\big) ^{\frac{\varepsilon }{2}}$. Heuristically, in…
A specific class of coagulation and fragmentation coefficients is considered for which the strength of the coagulation is balanced by that of the multiple fragmentation. Existence and uniqueness of mass-conserving solutions are proved when…
We prove several limit theorems that relate coalescent processes to continuous-state branching processes. Some of these theorems are stated in terms of the so-called generalized Fleming-Viot processes, which describe the evolution of a…
The global existence of mass-conserving weak solutions to the Safronov-Dubovskii coagulation equation is shown for the coagulation kernels satisfying the at most linear growth for large sizes. In contrast to previous works, the proof mainly…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
A global existence theorem on weak solutions is shown for the continuous coagulation equation with collisional breakage under certain classes of unbounded collision kernels and distribution functions. This model describes the dynamics of…
We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski's equations of coagulation for the solvable kernels $K(x,y)=2$, $x+y$ and $xy$. In addition to the known self-similar solutions with exponential tails, there…
We study coupled non-linear parabolic equations for a fluid described by a material density and a temperature, both functions of space and time. In one dimension, we find some stationary solutions corresponding to fixing the temperature on…
We consider systems of damped wave equations with a state-dependent damping coefficient and perturbed by a Gaussian multiplicative noise. Initially, we investigate their well-posedness, under quite general conditions on the friction.…
New weak and strong existence and weak and strong uniqueness results for multi-dimensional stochastic McKean--Vlasov equations are established under relaxed regularity conditions. Weak existence is a variation of Krylov's weak existence for…
Existence and uniqueness theorems for quantum stochastic differential equations with nontrivial initial conditions are proved for coefficients with completely bounded columns. Applications are given for the case of finite-dimensional…
A Smoluchowski type model of coagulation in a turbulent fluid is given, first expressed by means of a stochastic model, then in a suitable scaling limit as a deterministic model with enhanced diffusion in the velocity component. A precise…
Researchers have employed variations of the Smoluchowski coagulation equation to model a wide variety of both organic and inorganic phenomena and with relatively few known analytical solutions, numerical solutions play an important role in…
A modeling framework for the internal conformational dynamics and external mechanical movement of single biological macromolecules in aqueous solution at constant temperature is developed. Both the internal dynamics and external movement…
For one-dimensional many-body systems interacting via the \textit{Coulomb force} and with \textit{arbitrary} external potential energy, we derive (\textit{i}) the \textit{node coalescence condition} for the wave function. This condition…
We prove that the spatial coagulation equation with bounded coagulation rate is well-posed for all times in a given class of kernels if the convection term of the underlying particle dynamics has divergence bounded below by a positive…
A Stokes-type problem for a viscoelastic model of salt rocks is considered, and existence, uniqueness and regularity are investigated in the scale of $L^2$-based Sobolev spaces. The system is transformed into a generalized Stokes problem,…