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Entropy solutions for time-fractional porous medium type equations
Kerstin Schmitz, Petra Wittbold
In this paper we prove existence of entropy solutions to the time-fractional porous medium type equation, $$\partial_t[k\ast(u-u_0)]-\operatorname{div} (A(t,x)\nablaφ(u))=f\text{ i…
Bounded weak solutions of time-fractional porous medium type and more general nonlinear and degenerate evolutionary integro-differential equations
Petra Wittbold, Patryk Wolejko, Rico Zacher
We prove existence of a bounded weak solution to a degenerate quasilinear subdiffusion problem with bounded measurable coefficients that may explicitly depend on time. The kernel i…
Entropy solutions of doubly nonlinear fractional Laplace equations
N. Grossekemper, P. Wittbold, A. Zimmermann
In this contribution, we study a class of doubly nonlinear elliptic equations with bounded, merely integrable right-hand side on the whole space . The equation is dri…
Multi-dimensional scalar balance laws with discontinuous flux
Piotr Gwiazda, Agnieszka Swierczewska-Gwiazda, Petra Wittbold +1
We consider the problem of existence of entropy weak solutions to scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect both to th…