Semilinear Parabolic Equations with Nonmonotone Nonlinearity

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  • Semilinear Parabolic Equations with Non

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A semilinear evolution equation of the type u_t-Δu-g_1(x, t, u)+g_2(x, t, u)=f on Ω×(0,T) is studied in the space L^1(Ω), where Ω is a bounded domain in R^N, and g_1(x, t, r) and g_2(x, t, r) are monotone continuous with respect to r and measurable with respect to x and t. An existence theorem for the initial value problem associated to this semilinear equation is proved. We then apply this existence result to solve the problem u_t-Δu-u^p+u^q=ν and u(・, 0)=μ with measures ν and μ.

A semilinear evolution equation of the type u_t-Δu-g_1(x, t, u)+g_2(x, t, u)=f on Ω×(0,T) is studied in the space L^1(Ω), where Ω is a bounded domain in R^N, and g_1(x, t, r) and g_2(x, t, r) are monotone continuous with respect to r and measurable with respect to x and t. An existence theorem for the initial value problem associated to this semilinear equation is proved. We then apply this existence result to solve the problem u_t-Δu-u^p+u^q=ν and u(・, 0)=μ with measures ν and μ.

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