Article Contents
Article Contents

# On the heat equation with concave-convex nonlinearity and initial data in weak-$L^p$ spaces

• We analyze the local well-posedness of the initial-boundary value problem for the heat equation with nonlinearity presenting a combined concave-convex structure and taking the initial data in weak-$L^{p}$ spaces. Moreover we give a new uniqueness class and obtain some results about the behavior of the solutions near $t=0^{+}.$
Mathematics Subject Classification: Primary: 35K05, 35K55, 35A05; Secondary: 42B35.

 Citation:

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